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

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 the options
Answer: c

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

Question: The distance of point P(3, 4,5) from the yz-plane is
a) 3 units
b) 4 units
c) 5 units
d) 550 units
Answer: a

Question: The distance of the point P(a, b, c) from the x-axis is
a) √(b² + c²)
b) √(a² + c²)
c) √(a² + b²)
d) None of the options
Answer: a

Question: What are coordinates of the point equidistant from the points (a, 0, 0), (0, a, 0), (0, 0, a) and (0, 0, 0) ?
a) (a/3 , a/3 , a/3)
b) (a/2 , a/2 , a/2)
c) (a, a, a)
d) (2a, 2a, 2a)
Answer: b

Question: What is the length of foot of perpendicular drawn from the point P(3 ,4 ,5) on y-axis?
a) √41
b) √34
c) 5
d) None of the options
Answer: b

Question: Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, 4, 6) in the ratio 2 : 3 externally.
a) (– 8, – 17, 3)
b) (– 8, 17, 3)
c) (8, – 17, 3)
d) None of the options
Answer: b

Question: Find the ratio in which the YZ-plane divides the line segment formed by joining the points (– 2, 4, 7) and (3, – 5, 8).
a) externally 2 : 3
b) internally 2 : 3
c) internally 3 : 2
d) externally 3 : 2
Answer: b

Question: L is the foot of the perpendicular drawn from a point P(6, 7, 8) on the xy-plane. What are the coordinates of point L?
a) (6, 0, 0)
b) (6, 7, 0)
c) (6, 0, 8)
d) None of the options
Answer: b

Question: Find the length of the medians of the triangle with vertices A(0,0,6),B(0,4,0) and C(6,0,0).
a) 7, 7,√34
b) 7, 8, √34
c) 7 9 34 ,
d) None of the options
Answer: a

Question: Three vertices of a parallelogram ABCD are A (1,2, 3)B (-1,-2,-1) B(-1,-2,-1) and C(2,3,2) find the fourth vertex D.
a) (– 4, – 7, – 6)
b) (4, 7, 6)
c) (4, 7, – 6)
d) None of the options
Answer: a

Question: Find the equation of set points P such that PA2 + PB2 = 2K2, where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively :
a) K² – 109
b) 2K ² – 109
c) 3K² – 109
d) 4K ² – 10
Answer: b

Question: The points (5, 2, 4), (6, –1, 2) and (8, –7, k) are collinear if k is equal to
a) –2
b) 2
c) 3
d) –1
Answer: a

Question: If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is
a) 2√3
b) 3√2
c) √2
d) √3
Answer: a

Question: A plane is parallel xy-plane, so it is perpendicular to
a) z-axis
b) y-axis
c) x-axis
d) None of the options
Answer: a

Question: The point ( -2,3,-4) lies in the
a) first octant
b) seventh octant
c) second octant
d) eight octant
Answer: b

Question: The points (5, – 4, 2),(4,– 3, 1),(7,-6,4) and (8, – 7, 5) are the vertices of
a) a rectangle
b) a square
c) a parallelogram
d) None of the options
Answer: c

Question: In three dimensional space the path of a point whose distance from the x-axis is 3 times its distance from the yz-plane is:
a) y² + z² = 9x²
b) x² + y² =3z²
c) x² + z² = 3y²
d) y² – z² = 9x²
Answer: a

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: 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 the options
Answer: b

Question: The points A(5,1,) B(7,-4,7), C(1,-6,10) and D(-1,-3,4) are vertices of a
a) square
b) rhombus
c) rectangle
d) None of the options
Answer: b

Question: If x²+y²=1,then the distance from the point ((xy,√1-x²-y²) to the origin is
a) 1
b) – 1
c) 0
d) 2
Answer: a

Question: L is the foot of the perpendicular drawn from a point P( (3,4,5) on the xy-plane. The coordinates of point L are
a) (3, 0, 0)
b) (0, 4, 5)
c) (3, 0, 5)
d) None of the options
Answer: d

Question: Find the centroid of a triangle, the mid-point of whose sides are D(1,2,-3), E(3,0,1) and F(-1,1,-4).
a) (1, 1, 2)
b) (1, 1, – 2)
c) (– 1, –1, –2)
d) (1, –1, –2)
Answer: b

Question: If A and B be the points (3, 4, 5) and (– 1, 3, – 7) respectively, find the equation of the set of points P such that(PA)²+ (PB)²=k² , where K is a constant.
a) 2(x²+y²+z²) +4x+14y+az+109-k²=0
b) 2(x²+y²+z²)-4x-14y+AZ+109-k²=0
c) x²+y²+z²+4x+14y+az+109-k²=0
d) None of the options
Answer: b

Question: For every point P(x, y, z) on the xy-plane,
a) x = 0
b) y = 0
c) z = 0
d) None of the options
Answer: c

Question: If x-coordinate of a point P of line joining the points Q( 2, 2, 1) and R( 5,2 ,2) is 4, then the z-coordinate of P is
a) –2
b) –1
c) 1
d) 2
Answer: b

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: The coordinates of a point which is equidistant from the points (0, 0, 0), (a, 0, 0,),( 0,b,0), ) (0,0,c) are given by
a) (a/2,b/2,c/2)
b) (-a/1,b/2,c/2)
c) (a/2,-b/2,c/2)
d) (-a/2,b/2,c/2)
Answer: a

Question: If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is
a) 6
b) 2√2
c) 2√3
d) None of the options
Answer: b

Question: The locus of a point for which y = 0, z = 0 is
a) equation of x-axis
b) equation of y-axis
c) equation of z-axis
d) None of the options
Answer: a

Question: What is the perpendicular distance of the point P(6, 7, 8) from xy-plane?
a) 8
b) 7
c) 6
d) none of the options
Answer: a

Question: The point equidistant from the four points (0,0, 0), (3/2, 0, 0), (0,5/2, 0) and (0, 0, 7/2) is:
a) (2/3 , 1/3 , 2/5)
b) (3, 2, 3/5)
c) (3/4 , 5/4 , 7/4)
d) (1,0, 1/2)
Answer: c

Question: What is the shortest distance of the point (1, 2, 3) from x- axis ?
a) 1
b) √6
c) √13
d) √14
Answer: c

Question: If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is
a) 6
b) 2√2
c) 2√3
d) None of the options
Answer: b

Question: If the distance between the points ( a,01,) and (0,1,2) ) is √27, then the value of a is
a) 5
b) ± 5
c) – 5
d) None of the options
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 – 4x + 2z + 6 = 0
c) y² – 2y – 4x + 2z + 6 = 0
d) x² + y² – z² = 0
Answer: c

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

Question: L is the foot of the perpendicular drawn from a point (6, 7, 8) on x-axis. The coordinates of L are
a) (6, 0, 0)
b) (0, 7, 0)
c) (0, 0, 8)
d) None of the options
Answer: a

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 point equidistant from the four points (0,0, 0), (3/2, 0, 0), (0,5/2, 0) and (0, 0, 7/2) is:
a) (2/3 , 1/3 , 2/5)
b) (3, 2, 3/5)
c) (3/4 , 5/4 , 7/4)
d) (1/2,0, -1)
Answer: c

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

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: The three vertices of a parallelogram taken in order are (–1, 0), (3, 1) and (2, 2) respectively. Find the coordinate of the fourth vertex.
a) (2,1)
b) (–2,1)
c) (1,2)
d) (1,–2)
Answer: b

Question: Distance of the point (1, 2, 3) from the coordinate axes are
a) 13,10, 5
b) √13 √10 √5
c) √5 √13 √10
d) 1/√13,1/√10,1/√5
Answer: b

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 :
1. R divides PQ internally in the ratio 3 : 2
2. R divides PQ externally in the ratio 3 : 2
3. Q divides PR internally in the ratio 1 : 2
Which of the statements given above is/are correct ?
a) 1 only
b) 2 only
c) 1 and 3
d) 2 and 3
Answer: d