Class 11 Mathematics Introduction To Three-Dimensional Geometry MCQs Set 03

Question: If a parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes, then the length of the diagonal is
(a) 7 units
(b) 5 units
(c) 8 units
(d) 3 units
Answer: a

Question: The ratio in which the join of ( 2, 1, 5) and (3, 4, 3) is divided by the plane (x + y – z) = 1/2 is:
(a) 3 : 5
(b) 5 : 7
(c) 1 : 3
(d) 4 : 5
Answer: b

Question: ABC is a triangle and AD is the median. If the coordinates of A are ( 4, 7, – 8)and the coordinates of centroid of the triangle ABC are (1, 1, 1), what are the coordinates of D?
(a) (– 1/2 ,2,11)
(b) (– 1/2 , –2, 11/2)
(c) (–1, 2, 11)
(d) (–5, –11, 19)
Answer: b

Question: What is the locus of a point which is equidistant from the points (1, 2, 3) and (3, 2, – 1) ?
(a) x + z = 0
(b) x – 3z = 0
(c) x – z = 0
(d) x – 2z = 0
Answer: d

Question: If L, M and N are the feet of perpendiculars drawn from the point P(3, 4, 5) on the XY, YZ and ZX-planes respectively, then
(a) distance of the point L from the point P is 5 units.
(b) distance of the point M from the point P is 3 units.
(c) distance of the point N from the point P is 4 units.
(d) All of the above.
Answer: d

Question: Find the coordinates of the point which is three fifth of the way from (3, 4, 5) to (– 2, – 1, 0).
(a) (1, 0, 2)
(b) (2, 0, 1)
(c) (0, 2, 1)
(d) (0, 1, 2)
Answer: d

Question: The locus of a point for which x = 0 is
(a) xy-plane
(b) yz-plane
(c) zx-plane
(d) None of these
Answer: b

Question: The ratio in which the join of points (1, –2, 3) and (4, 2, –1) is divided by XOY plane is
(a) 1 : 3
(b) 3 : 1
(c) –1 : 3
(d) None of these
Answer: b

Question: The perpendicular distance of the point P(6, 7, 8) from xy-plane is
(a) 8
(b) 7
(c) 6
(d) None of these
Answer: a

Question: The ratio, in which YZ-plane divides the line segment joining the points (4, 8, 10) and (6, 10, – 8), is
(a) 2 : 3 (externally)
(b) 2 : 3 (internally)
(c) 1 : 2 (externally)
(d) 1 : 2 (internally)
Answer: a

Question: The ratio in which the line joining the points (2,4, 5) and (3, 5, – 4) is internally divided by the xy-plane is
(a) 5 : 4
(b) 3 : 4
(c) 1 : 2
(d) 7 : 5
Answer: a

Question: For every point P(x, y, z) on the x-axis (except the origin),
(a) x = 0, y = 0, z ≠ 0
(b) x = 0, z = 0, y ≠ 0
(c) y = 0, z = 0, x ≠ 0
(d) None of these
Answer: c

Question: The mid-points of the sides of a triangle are (5, 7, 11),(0, 8, 5) and (2, 3, – 1), then the vertices are
(a) (7, 2, 5), (3, 12, 17), (– 3, 4, – 7)
(b) (7, 2, 5), (3, 12, 17), (3, 4, 7)
(c) (7, 2, 5), (– 3, 11, 15), (3, 4, 8)
(d) None of the above
Answer: a

Question: Given that A(3, 2, – 4), B(5, 4 – 6) and C(9, 8, – 10) are collinear. Ratio in which B divides AC is 1 : m. The value of m is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: a

Question: If A(3, 2, 0), B(5, 3, 2) and C(– 9, 6, – 3) are three points forming a triangle and AD, the bisector of ∠BAC, meets BC in D, then the coordinates of the point D are 
(a) (17/8 , 57/8 ,17/8)
(b) (19/8 , 57/16 ,17/16)
(c) (8/17 , 8/19 ,17/8)
(d) None of these
Answer: b

Question: The points A(4, – 2, 1), B(7, – 4, 7), C (2, – 5, 10) and D (– 1, – 3, 4) are the vertices of a
(a) tetrahedron
(b) parallelogram
(c) rhombus
(d) square
Answer: b

Question: Let L, M, N be the feet of the perpendiculars drawn from a point P(7, 9, 4) on the x, y and z-axes respectively. The coordinates of L, M and N respectively are
(a) (7, 0, 0), (0, 9, 0), (0, 0, 4)
(b) (7, 0, 0), (0, 0, 9), (0, 4, 0)
(c) (0, 7, 0), (0, 0, 9), (4, 0, 0)
(d) (0, 0, 7), (0, 9, 0), (4, 0, 0)
Answer: a

Question: The coordinates of the points which trisect the line segment joining the points P(4, 2, – 6) and Q(10, – 16, 6) are
(a) (6, – 4, – 2) and (8, 10, – 2)
(b) (6, – 4, – 2) and (8, – 10, 2)
(c) (–6, 4, 2) and (– 8, 10, 2)
(d) None of these
Answer: b

Question: Point (–3, 1, 2) lies in
(a) Octant I
(b) Octant II
(c) Octant III
(d) Octant IV
Answer: b

Question: If the point A (3, 2, 2) and B(5, 5, 4) are equidistant from P, which is on x-axis, then the coordinates of P are
(a) (39/4 ,2,0)
(b) (49/4 ,2,0)
(c) (39/4,0,0)
(d) (49/4 ,0,0)
Answer: d

Question: If the sum of the squares of the distance of the point ( x, y, z) from the points ( a, 0, 0) and ( –a , 0, 0) is 2c², then which one of the following is correct?
(a) x² + a² = 2c² – y² – z²
(b) x² + a² = c²– y2 – z²
(c) x² – a² = c²– y2 – z²
(d) x² + a² = c²+ y2 + z²
Answer: b

Question: The equation of locus of a point whose distance from the y-axis is equal to its distance from the point (2, 1, –1) is
(a) x² + y² + z² = 6
(b) x² – 4x² + 2z² + 6 = 0
(c) y² – 2y² – 4x² + 2z + 6 = 0
(d) x² + y² – z² = 0
Answer: c

STATEMENT TYPE QUESTIONS

Question: P(a, b, c); Q (a + 2, b + 2, c – 2) and R (a + 6, b + 6, c – 6) are collinear.
Consider the following statements :
I. R divides PQ internally in the ratio 3 : 2
II. R divides PQ externally in the ratio 3 : 2
III. Q divides PR internally in the ratio 1 : 2
Which of the statements given above is/are correct ?
(a) Only I
(b) Only II
(c) I and III
(d) II and III
Answer: d

Question: Consider the following statements
I. The x-axis and y-axis together determine a plane known as xy-plane.
II. Coordinates of points in xy-plane are of the form (x1, y1, 0). 
Choose the correct option.
(a) Only I is true.
(b) Only II is true.
(c) Both are true.
(d) Both are false.
Answer: c

Question: Consider the following statement
I. Any point on X-axis is of the form (x, 0, 0)
II. Any point on Y-axis is of the form (0, y, 0)
III. Any point on Z-axis is of the form (0, 0, z)
Choose the correct option.
(a) Only I and II are true.
(b) Only II and III are true.
(c) Only I and III are true.
(d) All are true.
Answer: d