Class 11 Mathematics 3D Plane MCQs Set 02

LEVEL - I

Cartesian equation of a plane:

Question. If the equation of the plane passing through the points (1, 2, 3), (-1, 2, 0) and perpendicular to the ZX-plane is \( ax + by + cz + d = 0 \) \( (a > 0) \) then
(a) \( a = 0 \) and \( c = 0 \)
(b) \( a + d = 0 \)
(c) \( c + d - 5 = 0 \)
(d) \( a + c + d - 4 = 0 \)
Answer: (d) \( a + c + d - 4 = 0 \)

Question. The equation of the plane through the line of intersection of planes \( ax + by + cz + d = 0 \), \( a'x + b'y + c'z + d' = 0 \) and parallel to the lines \( y = 0 = z \) is
(a) \( (ab' - a'b)x + (bc' - b'c)y + (ad' - a'd) = 0 \)
(b) \( (ab' - a'b)y + (ac' - a'c)z + (ad' - a'd) = 0 \)
(c) \( (ab' - a'b)x + (bc' - b'c)z + (ad' - a'd) = 0 \)
(d) \( (ab' - a'b)x - (bc' - b'c)y + (ad' + a'd) = 0 \)
Answer: (b) \( (ab' - a'b)y + (ac' - a'c)z + (ad' - a'd) = 0 \)

Question. A plane \( \pi \) passes through the point (1, 1, 1). If b, c, a are the dr’s of a normal to the plane, where a, b, c \( (a < b < c) \) are the prime factors of 2001, then the equation of the plane \( \pi \) is
(a) \( 29x + 31y + 3z = 63 \)
(b) \( 23x + 29y - 29z = 23 \)
(c) \( 23x + 29y + 3z = 55 \)
(d) \( 31x + 27y + 3z = 71 \)
Answer: (c) \( 23x + 29y + 3z = 55 \)

Question. The dr’s of a normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle of \( \frac{\pi}{4} \) with the plane \( x + y = 3 \) are
(a) \( 1, \sqrt{2}, 1 \)
(b) \( 1, 1, \sqrt{2} \)
(c) \( 1, 1, 2 \)
(d) \( \sqrt{2}, 1, 1 \)
Answer: (b) \( 1, 1, \sqrt{2} \)

Question. Let \( A(1, 1, 1), B(2, 3, 5) \) and \( C(-1, 0, 2) \) be three points, then equation of a plane parallel to the plane ABC which is at a distance 2 units is
(a) \( 2x - 3y + z + 2\sqrt{14} = 0 \)
(b) \( 2x - 3y + z - \sqrt{14} = 0 \)
(c) \( 2x - 3y + z + 2 = 0 \)
(d) \( 2x - 3y + z - 2 = 0 \)
Answer: (a) \( 2x - 3y + z + 2\sqrt{14} = 0 \)

Intercept form of a plane:

Question. A variable plane intersects the coordinate axes at A, B, C and is at a constant distance 'p' from 0(0, 0, 0). Then the locus of the centroid of the tetrahedron OABC is
(a) \( \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{1}{p^2} \)
(b) \( \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{4}{p^2} \)
(c) \( \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{16}{p^2} \)
(d) \( \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = 16p^2 \)
Answer: (c) \( \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{16}{p^2} \)

Question. The equation to the plane through the line of intersection of \( 2x + 3y + z - 2 = 0 \), \( x - y + z + 4 = 0 \) such that each plane is at a distance of 2 unit from the origin is
(a) \( x + y + z + 13 = 0, x + y + z - 3 = 0 \)
(b) \( 2x + y - 2z + 3 = 0, 2x - y - 2z - 3 = 0 \)
(c) \( 15x - 12y + 16z + 50 = 0, x + 2y + 2z - 6 = 0 \)
(d) \( x - y + 2z - 13 = 0, x + y - z - 3 = 0 \)
Answer: (c) \( 15x - 12y + 16z + 50 = 0, x + 2y + 2z - 6 = 0 \)

Question. The equation of the plane which is parallel to X-axis and making intercepts 3 and 8 on Y and Z-axes respectively is
(a) \( 3y + 8z = 24 \)
(b) \( 3y - 8z = 24 \)
(c) \( 8y - 3z = 24 \)
(d) \( 8y + 3z = 24 \)
Answer: (d) \( 8y + 3z = 24 \)

Question. The sum of the intercepts of the plane which bisects the line segment joining (0, 1, 2) and (2, 3, 0) perpendicularly is
(a) 2
(b) 4
(c) 6
(d) 12
Answer: (a) 2

Question. A plane meets the coordinate axes at A, B, C so that the centroid of the triangle ABC is (1, 2, 4). Then the equation of the plane is
(a) \( x + 2y + 4z = 12 \)
(b) \( 4x + 2y + z = 12 \)
(c) \( x + 2y + 4z = 3 \)
(d) \( 4x + 2y + z = 3 \)
Answer: (b) \( 4x + 2y + z = 12 \)

Question. The reflection of the plane \( 2x - 3y + 4z - 3 = 0 \) in the plane \( x - y + z - 3 = 0 \) is the plane
(a) \( 4x - 3y + 2z - 15 = 0 \)
(b) \( x - 3y + 2z - 15 = 0 \)
(c) \( 4x + 3y - 2z + 15 = 0 \)
(d) \( 4x + 3y + 2z + 15 = 0 \)
Answer: (a) \( 4x - 3y + 2z - 15 = 0 \)

LEVEL - II

Cartesian equation of a plane:

Question. The d.r's of the line of intersection of the planes \( x + y + z - 1 = 0 \) and \( 2x + 3y + 4z - 7 = 0 \) are
(a) 1, 2, -3
(b) 2, 1, -3
(c) 4, 2, -6
(d) 1, -2, 1
Answer: (d) 1, -2, 1

Question. The vertices of a tetrahedron are A(3, 4, 2), B(1, 2, 1), C(4, 1, 3), D(-1, -1, 3). The height of A above the base BCD.
(a) \( \frac{27}{\sqrt{237}} \)
(b) \( \frac{23}{\sqrt{237}} \)
(c) \( \frac{20}{\sqrt{237}} \)
(d) \( \frac{27}{\sqrt{247}} \)
Answer: (b) \( \frac{23}{\sqrt{237}} \)

Question. The equation of the plane which passes through the line of intersection of the planes \( 2x - y = 0 \) and \( 3z - y = 0 \) and is perpendicular to the plane \( 4x + 5y - 3z = 8 \) is
(a) \( 28x - 17y + 9z = 0 \)
(b) \( 28x + 17y + 9z = 0 \)
(c) \( 2x + 17y + 9z = 0 \)
(d) \( 2x - y - z = 0 \)
Answer: (a) \( 28x - 17y + 9z = 0 \)

Question. The dr’s of a normal to the plane passing through (0, 0, 1), (0, 1, 2) and (1, 2, 3) are
(a) (0, 1, -1)
(b) (1, 0, -1)
(c) (0, 0, -1)
(d) (1, 0, 0)
Answer: (a) (0, 1, -1)

Question. The plane \( 2x + 3y + kz - 7 = 0 \) is parallel to the line whose direction ratios are (2, -3, 1) then k =
(a) 5
(b) 8
(c) 1
(d) 0
Answer: (a) 5

Intercept form of a plane:

Question. A variable plane is at a constant distance 3p from the origin and meets the axes in A, B and C. The locus of the centroid of the triangle ABC is
(a) \( x^{-2} + y^{-2} + z^{-2} = p^{-2} \)
(b) \( x^{-2} + y^{-2} + z^{-2} = 4p^{-2} \)
(c) \( x^{-2} + y^{-2} + z^{-2} = 16p^{-2} \)
(d) \( x^{-2} + y^{-2} + z^{-2} = 9p^{-2} \)
Answer: (a) \( x^{-2} + y^{-2} + z^{-2} = p^{-2} \)

Question. The equation of the plane through the line of intersection of the planes \( x - 2y + 3z - 1 = 0 \), \( 2x + y + z - 2 = 0 \) and the point (1, 2, 3) is
(a) \( 7x - 9y + 8z = 0 \)
(b) \( 7x + y + 8z = 0 \)
(c) \( x + 3y - 2z - 1 = 0 \)
(d) \( x - 3y - 2z + 1 = 0 \)
Answer: (c) \( x + 3y - 2z - 1 = 0 \)

Question. The equation of the plane which is parallel to Y-axis and making intercepts of lengths 3 and 4 on X-axis and Z-axis is
(a) \( 2x + 2z = 20 \)
(b) \( 4x + 3z = 12 \)
(c) \( 4x - 3z = 12 \)
(d) \( 6x + 13z = 15 \)
Answer: (b) \( 4x + 3z = 12 \)

Question. If 5, 7, 6 are the sums of the X, Y intercepts; Y, Z intercepts, Z, X intercepts respectively of a plane then the perpendicular distance from the origin to that plane is
(a) \( \frac{144}{61} \)
(b) \( \frac{12}{\sqrt{61}} \)
(c) \( \frac{\sqrt{61}}{12} \)
(d) \( \frac{61}{144} \)
Answer: (b) \( \frac{12}{\sqrt{61}} \)

Question. The equation of the plane through the line of intersection of the planes \( 2x + 3y + 4z - 7 = 0 \), \( x + y + z - 1 = 0 \) and perpendicular to the plane \( x - 5y + 3z - 2 = 0 \) is
(a) \( 7x - y - 6z - 17 = 0 \)
(b) \( x - y - 6z - 27 = 0 \)
(c) \( x + y + 2z - 3 = 0 \)
(d) \( x + y + 6z - 27 = 0 \)
Answer: (c) \( x + y + 2z - 3 = 0 \)

Question. The equations of bisectors of angles between YZ-plane and XZ-plane is
(a) \( x - z = 0, x + z = 0 \)
(b) \( x - z + 2 = 0 \)
(c) \( x + z = 0, x - z = 0 \)
(d) \( x + y = 0, x - y = 0 \)
Answer: (d) \( x + y = 0, x - y = 0 \)

LEVEL -III

Question. If the angles made by the normal of the plane \( 2x + 3y - 4z - 16 = 0 \) with the coordinates axes X, Y, Z are \( \cos^{-1} k_1, \cos^{-1} k_2, \cos^{-1} k_3 \), then \( k_1, k_2, k_3 \) respecitvely are
(a) \( \frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}} \)
(b) \( \frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, -\frac{4}{\sqrt{29}} \)
(c) \( \frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, -\frac{4}{\sqrt{29}} \)
(d) \( \frac{1}{2}, \frac{1}{3}, -\frac{1}{4} \)
Answer: (c) \( \frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, -\frac{4}{\sqrt{29}} \)

Question. The two planes represented by \( 12x^2 - 2y^2 - 6z^2 - 7yz + 6zx - 2xy = 0 \) are
(a) \( 2x + y + 2z = 0, 6x - 2y + 3z = 0 \)
(b) \( 2x - y + 2z = 0, 6x + 2y - 3z = 0 \)
(c) \( 2x - y + 2z + 4 = 0, 6x + 2y - 3z = 0 \)
(d) \( 2x - y + 2z = 0, 6x + 2y - 3z + 1 = 0 \)
Answer: (b) \( 2x - y + 2z = 0, 6x + 2y - 3z = 0 \)

Question. If the plane \( 4(x - 1) + k(y - 2) + 8(z - 5) = 0 \) contains the line \( \frac{x-1}{2} = \frac{y-2}{4} = \frac{z-5}{3} \), then k is
(a) 2
(b) 4
(c) -8
(d) 8
Answer: (c) -8

Question. If the plane \( 3(x - 2) + (y - 2) + 6(z + 3) = 0 \) contains the line \( \frac{x-2}{a} = \frac{y-2}{b} = \frac{z+3}{1} \) whose inclination with X-axis is \( 60^\circ \), then it satisfies the equation
(a) \( 26a^2 + 36a + 37 = 0 \)
(b) \( 36a^2 + 37 = 0 \)
(c) \( 36a^2 + 37a + 36 = 0 \)
(d) \( a + 3 = 0 \)
Answer: (a) \( 26a^2 + 36a + 37 = 0 \)

Question. The angle between the planes represented by \( 2x^2 - 6y^2 - 12z^2 + 18yz + 2zx + xy = 0 \) is
(a) \( \cos^{-1} \left( \frac{16}{21} \right) \)
(b) \( \cos^{-1} \left( \frac{17}{21} \right) \)
(c) \( \cos^{-1} \left( \frac{19}{21} \right) \)
(d) \( \frac{\pi}{2} \)
Answer: (a) \( \cos^{-1} \left( \frac{16}{21} \right) \)

Question. If the equation of the plane passing through the line of intersection of the planes \( ax + by + cz + d = 0, a_1x + b_1y + c_1z + d_1 = 0 \) and perpendicular to the XY-plane is \( px + qy + rz + s = 0 \) then S =
(a) \( dc_1 - d_1c \)
(b) \( dc_1 + d_1c \)
(c) \( dd_1 + cc_1 \)
(d) \( aa_1 + bb_1 + cc_1 \)
Answer: (a) \( dc_1 - d_1c \)

Question. If the points (1, 1, -3) and (1, 0, -3) lie on opposite sides of the plane \( x + y + 3z + d = 0 \) then
(a) \( d < 7 \)
(b) \( d > 8 \)
(c) \( 7 < d < 8 \)
(d) \( d < 7 \) or \( d > 8 \)
Answer: (c) \( 7 < d < 8 \)

Question. P is a point such that the sum of the squares of its distances from the planes \( x + y + z = 0 \), \( x + y - 2z = 0, x - y = 0 \) is 5 then the locus of P is
(a) \( x^2 + y^2 + z^2 = 10 \)
(b) \( x^2 + y^2 + z^2 = 25 \)
(c) \( x^2 + y^2 + z^2 = 5 \)
(d) \( x^2 + y^2 + z^2 = 50 \)
Answer: (c) \( x^2 + y^2 + z^2 = 5 \)

Question. The areas of triangles formed by a plane with the positive \( X, Y; Y, Z; Z, X \) axes respectively are 12, 9, 6 square units then the equation of the plane is
(a) \( \frac{x}{4} + \frac{y}{6} + \frac{z}{3} = 1 \)
(b) \( \frac{x}{6} + \frac{y}{3} + \frac{z}{4} = 1 \)
(c) \( \frac{x}{4} + \frac{y}{4} + \frac{z}{6} = 1 \)
(d) \( \frac{x}{3} + \frac{y}{6} + \frac{z}{4} = 1 \)
Answer: (a) \( \frac{x}{4} + \frac{y}{6} + \frac{z}{3} = 1 \)

Question. The plane \( ax + by + cz + (-3) = 0 \) meet the co-ordinate axes in A, B, C. Then centroid of the triangle is
(a) \( (3a, 3b, 3c) \)
(b) \( (\frac{3}{a}, \frac{3}{b}, \frac{3}{c}) \)
(c) \( (\frac{a}{3}, \frac{b}{3}, \frac{c}{3}) \)
(d) \( (\frac{1}{a}, \frac{1}{b}, \frac{1}{c}) \)
Answer: (d) \( (\frac{1}{a}, \frac{1}{b}, \frac{1}{c}) \)

Question. Equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes \( x + 2y + 3z = 5 \) and \( 3x + 3y + z = 0 \) is
(a) \( 7x + 8y - 3z = 0 \)
(b) \( 7x - 8y - 3z = -37 \)
(c) \( 7x - 8y + 3z + 25 = 0 \)
(d) \( 7x + 8y + 3z = 23 \)
Answer: (c) \( 7x - 8y + 3z + 25 = 0 \)

Question. If P= (0, 1, 0) and Q = (0, 0, 1) then the projection of PQ on the plane \( x + y + z = 3 \) is
(a) 2
(b) \( \sqrt{2} \)
(c) 3
(d) \( \sqrt{3} \)
Answer: (b) \( \sqrt{2} \)

Question. A parallelopiped is formed by the planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes. The length of diagonal of the parallelopiped is
(a) 7
(b) \( \sqrt{38} \)
(c) \( \sqrt{155} \)
(d) \( \sqrt{7} \)
Answer: (a) 7

LEVEL -IV

Question. Match the following
List-I
a) The image of (2, 1, 4) in the plane \( 2x - y + z + 5 = 0 \)
b) The foot of perpendicular from (2, 1, 4) in the plane \( 2x - y + z + 5 = 0 \)
c) The point lying on \( 2x - y + z + 5 = 0 \)

List-II
i) \( (-2, 3, 2) \)
ii) \( (-4, 1, 4) \)
iii) \( (-6, 5, 0) \)

Which of the following is correct?
(a) a-iii, b-ii, c-i
(b) a-i, b-iii, c-ii
(c) a-i, b-ii, c-iii
(d) a-iii, b-i, c-ii
Answer: (c) a-i, b-ii, c-iii

Question. Observe the following Statements:
Statement I : The image of (0, 0, 0) in the plane \( 2x - 3y + 6z - 49 = 0 \) is (4, -6, 12)
Statement II : The foot of the perpendicular from (1, 2, 3) to the plane \( x + y - z - 9 = 0 \) is (3, 4, -1)

Which of the following is correct?
(a) I is true, II is true
(b) I is true, II is false
(c) Both I and II are false
(d) I is false, II is true
Answer: (a) I is true, II is true

Question. Equation of the plane passing through the point (-1,3,2) and perpendicular to each of the planes \( x + 2y + 3z = 5 \) and \( 3x + 3y + z = 0 \) is
(a) \( 7x + 8y - 3z = 0 \)
(b) \( 7x - 8y - 3z = -37 \)
(c) \( 7x - 8y + 3z + 25 = 0 \)
(d) \( 7x + 8y + 3z = 23 \)
Answer: (c) \( 7x - 8y + 3z + 25 = 0 \)

Question. If P = (0,1,0) and Q = (0,0,1) then the projection of PQ on the plane \( x + y + z = 3 \) is
(a) 2
(b) \( \sqrt{2} \)
(c) 3
(d) \( \sqrt{3} \)
Answer: (b) \( \sqrt{2} \)

Question. A parallelopiped is formed by the planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes. The length of diagonal of the paralleopiped is
(a) 7
(b) \( \sqrt{38} \)
(c) \( \sqrt{155} \)
(d) \( \sqrt{7} \)
Answer: (a) 7
 

LEVEL-V

Question. Match the following:
List-I
a) The image of (2, 1, 4) in the plane \( 2x - y + z + 5 = 0 \)
b) The foot of perpendicular from (2, 1, 4) in the plane \( 2x - y + z + 5 = 0 \)
c) The point lying on \( 2x - y + z + 5 = 0 \)
List-II
i) \( (-2, 3, 2) \)
ii) \( (-4, 1, 4) \)
iii) \( (-6, 5, 0) \)
Which of the following is correct?
(a) a-iii, b-ii, c-i
(b) a-i, b-iii, c-ii
(c) a-i, b-ii, c-iii
(d) a-iii, b-i, c-ii
Answer: (d) a-iii, b-i, c-ii

Question. Observe the following Statements:
Statement I : The image of (0, 0, 0) in the plane \( 2x - 3y + 6z - 49 = 0 \) is (4, -6, 12)
Statement II : The foot of the perpendicular from (1, 2, 3) to the plane \( x + y - 2z - 9 = 0 \) is (3, 4, -1)
Which of the following is correct?
(a) I is true, II is true
(b) I is true, II is false
(c) Both I and II are false
(d) I is false, II is true
Answer: (a) I is true, II is true

Question. \( \alpha, \beta, \gamma \) are the angles made by the normal of the plane \( 2x - 3y + 6z - 6 = 0 \) with axes X, Y, Z respectively. Match the cosine of the angles given in List I with corresponding values given in List II.
List-I
a) \( \cos \alpha \)
b) \( \cos \beta \)
c) \( \cos \gamma \)
List-II
i) 6 / 7
ii) \( -3 / 7 \)
iii) 2 / 7
The correct match from list I to list II is
(a) a-i, b-ii, c-iii
(b) a-ii, b-i, c-iii
(c) a-ii, b-iii, c-i
(d) a-iii, b-ii, c-i
Answer: (d) a-iii, b-ii, c-i

Question. The coordinates of a point P are (1, 2, -1). Match the plane given in List I with corresponding perpendicular distance from the point P to their planes given in List II.
List-I
a) \( 2x + y - z + 2 = 0 \)
b) \( x - y + 6z = 0 \)
c) \( 3x + 2y + 6z + 6 = 0 \)
List-II
i) 1
ii) \( \frac{7}{\sqrt{6}} \)
iii) \( \frac{7}{\sqrt{38}} \)
Which of the following is correct?
(a) a-ii, b-i, c-iii
(b) a-i, b-ii, c-iii
(c) a-iii, b-ii, c-i
(d) a-ii, b-iii, c-i
Answer: (d) a-ii, b-iii, c-i

ASSERTION & REASON

The following questions consist of two statements one labelled as Assertion (A) and the other labelled as Reason (R). You are to examine these two statements carefully and decide if the Assertion (A) and the Reason (R) are individually true and if so, whether the Reason (R) is the correct explanation for the given Assertion (A) select your answer to these items using the codes given below and then select the correct option
Codes:
(A) Both A and R are individually true and R is the correct explanation of A
(B) Both A and R individually true but R is not the correct explanation of A
(C) A is true but R is false
(D) A is false but R is true

Question. Assertion (A) : The equation of the plane through the intersection of the planes \( x + y + z = 6 \) and \( 2x + 3y + 4z + 5 = 0 \) and the point (4,4,4) is \( 29x + 23y + 17z = 276 \)
Reason (R) : Equation of the plane through the line of intersection of the planes \( P_1 = 0 \) and \( P_2 = 0 \) is \( P_1 + \lambda P_2 = 0 \ (\lambda \neq 0) \)
(a) A
(b) B
(c) C
(d) D
Answer: (a) A

Question. Assertion (A) : The points (2,1,5) and (3,4,3) lie on opposite side of the plane \( 2x + 2y - 2z - 1 = 0 \)
Reason (R) : The algebraic perpendicular distance from the given points to the line have opposite sign
(a) A
(b) B
(c) C
(d) D
Answer: (a) A

Question. The equation of the plane passing through the intersection of \( P_1 \) and \( P_2 \) and the point (3, 2, 1) is
(a) \( 3x - y + 2z - 9 = 0 \)
(b) \( x - 3y + 2z + 1 = 0 \)
(c) \( 2x - 3y + z - 1 = 0 \)
(d) \( 4x - 3y + 2z - 8 = 0 \)
Answer: (b) \( x - 3y + 2z + 1 = 0 \)

Question. Equation of the plane which passes through the point (-1, 3, 2) and is perpendicular to each of the planes \( P_1 \) and \( P_2 \) is
(a) \( x + 3y - 5z + 2 = 0 \)
(b) \( x + 3y + 5z - 18 = 0 \)
(c) \( x - 3y - 5z + 20 = 0 \)
(d) \( x - 3y + 5z = 0 \)
Answer: (c) \( x - 3y - 5z + 20 = 0 \)

Question. The equation of the acute angle bisector of planes \( P_1 \) and \( P_2 \) is
(a) \( x - 3y + 2z + 1 = 0 \)
(b) \( 3x + y - 5 = 0 \)
(c) \( x + 3y - 2z + 1 = 0 \)
(d) \( 3x + z + 7 = 0 \)
Answer: (a) \( x - 3y + 2z + 1 = 0 \)

Question. The equation of the bisector of angle of the planes \( P_1 \) and \( P_2 \) which not containing origin is
(a) \( x - 3y + 2z + 1 = 0 \)
(b) \( x + 3y = 5 \)
(c) \( x + 3y + 2z + 2 = 0 \)
(d) \( 3x + y = 5 \)
Answer: (d) \( 3x + y = 5 \)

Question. The image of plane \( P_1 \) in the plane mirror \( P_2 \) is
(a) \( x + 7y - 4z + 5 = 0 \)
(b) \( 3x + 4y - 5z + 9 = 0 \)
(c) \( 7x - y + 2z - 9 = 0 \)
(d) \( 7x + y + 9z + 9 = 0 \)
Answer: (c) \( 7x - y + 2z - 9 = 0 \)