# MCQs for Mathematics Class 11 with Answers Chapter 12 Introduction to Three Dimensional Geometry

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Introduction to Three-Dimensional Geometry with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

## Chapter 12 Introduction to Three-Dimensional Geometry MCQ with Answers Class 11 Mathematics

MCQ Questions Class 11 Mathematics Introduction to Three-Dimensional Geometry with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. What is the perpendicular distance of the point P(6, 7, 8) from xy-plane?
(a) 8 units
(b) 7 units
(c) 6 units
(d) 5 units

A

Question. If the origin is the centroid of the triangle with vertices A(3a, 4, –5), B(–2, 4b, 6) and C(6, 10, c), then find the values of a, b, c.
(a) -4/3 , -7/2 , -1
(b) 4/3 , 7/2 , 1
(c) -4/3 , -7/2 , 1
(d) None of these

A

Question. Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) in the ratio 2 : 3 externally.
(a) (–3, –14, 19)
(b) (3, 14, 19)
(c) (–3, –14, –19)
(d) (3, –14, –19)

A

Question. Find the equation of set of points P such that PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively.
(a) x2 + y2 + z2 – 4x – 14y + 4z = 2k2 – 109
(b) 2x2 + 2y2 – 2z2 – 4x – 14y – 4z = 2k2 + 109
(c) 2x2 + 2y2 + 2z2 – 4x – 14y + 4z = 2k2 – 109
(d) None of these

C

Question. The perpendicular distance of the point (8, 15, 6) from y-axis is
(a) 5 units
(b) 6 units
(c) 8 units
(d) 10 units

D

Question. Find the coordinates of a point which is equidistant from the four points O(0, 0, 0), A(l, 0, 0), B(0, m, 0) and C(0, 0, n).
(a) (l, m, n)
(b) (1/2,m/2,n/2)
(c) (1/2, m , n/2)
(d) (2l, 2m, 2n)

B

Question. A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10).
Find the coordinates of the point R.
(a) (1, 2, 9)
(b) (4, 2, 6)
(c) (8, 2, 5)
(d) (4, –2, 6)

D

Question. Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, –8) is divided by the yz-plane.
(a) 2 : 3 internally
(b) 2 : 3 externally
(c) 5 : 7 internally
(d) 5 : 7 externally

B

Question. The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, –6), respectively, then find the coordinates of the point C.
(a) (2, 1, 1)
(b) (1, 2, 1)
(c) (1, 1, 2)
(d) (1, 2, 2)

C

Question. Find the ratio in which the line segment joining the points (2, 4, 5) and (3, 5, –4) is divided by the xz-plane.
(a) 4 : 5 externally
(b) 2 : 3 externally
(c) 1 : 3 externally
(d) 4 : 5 internally

A

Question. Find the coordinate of the point P which is five-sixth of the way from A(–2, 0, 6) to B(10, –6, –12).
(a) (–8, 5, –9)
(b) (–8, –5, 9)
(c) (8, –5, –9)
(d) (8, 5, 9)

C

Question. Find the coordinates of the points which trisect the line segment AB where A(2, 1, –3) and B(5, –8, 3).
(a) (4, –5, 1), (3, –2, –1)
(b) (–4, 5, 1), (3, –2, –1)
(c) (–5, 4, 1), (3, 2, 1)
(d) (4, 5, –1), (3, 2, 1)

A

Question. M is the foot of the perpendicular drawn from the point A(6, 7, 8) on the yz-plane. What are the coordinates of point M?
(a) (6, 0, 0)
(b) (6, 7, 0)
(c) (6, 0, 8)
(d) (0, 7, 8)

D

Question. L is the foot of the perpendicular drawn from a point (3, 5, 6) on x-axis. The coordinates of L are
(a) (3, 0, 0)
(b) (0, 6, 0)
(c) (0, 0, 5)
(d) (0, 5, 6)

A

Question. Find the distance between the points P(1, –3, 4) and Q(–4, 1, 2).
(a) 5 units
(b) 5 3 units
(c) 3 5 units
(d) 2 2 units

C

Question. Equation of YOZ plane is
(a) x = 0
(b) y = 0
(c) z = 0
(d) None of these

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 these

A

Question. Find the equation of the set of the points P such that its distances from the points A(3, 4, –5) and B(–2, 1, 4) are equal.
(a) 10x + 6y – 18z – 29 = 0
(b) 10x + 18y – 6z – 29 = 0
(c) 5x + 3y – 9z – 29 = 0
(d) 10x + 6y – 18z – 45 = 0

A

Question. The equations of x-axis are
(a) x = 0, y = 0
(b) x = 0, z = 0
(c) y = 0, z = 0
(d) x = 0

C

Question. Find the point on x-axis which is equidistant from the point A(3, 2, 2) and B(5, 5, 4).
(a) (16, 0, 0)
(b) (5/4 , 0 ,0)
(c) (9, 0, 0)
(d) (49/4 , 0 ,0)

D

Question. Find the point on y-axis which is at a distance of 10 units from the point (1, 2, 3).
(a) (0, 4, 0)
(b) (0, 3, 0)
(c) (0, 2, 0)
(d) (0, –1, 0)

C

Question. Find the octant in which the points (–3, 1, 2) and (–3, 1, –2) lie respectively.
(a) second, fourth
(b) sixth, second
(c) fifth, sixth
(d) second, sixth

D

Question. The two vertices of a triangle are (4, 2, 1) and (5, 1, 4). If the centroid is (5, 2, 3), then the third vertex is
(a) (3, 4, 5)
(b) (6, 2, 3)
(c) (6, 3, 2)
(d) (6, 3, 4)

D

Question. Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is
(a) 3 : 1 internally
(b) 3 : 1 externally
(c) 2 : 1 internally
(d) 2 : 1 externally

B

Question. If P(3, 2, – 4), Q(5, 4, – 6) and R(9, 8, – 10) are collinear, then R divides PQ in the ratio
(a) 3 : 2 internally
(b) 3 : 2 externally
(c) 2 : 1 internally
(d) 2 : 1 externally

B

Question. Mid-point of the line joining the points (– 1, 2, 3) and (2, – 1, 3) is
(a) (1, 1, 6)
(b) (1/2, 1/2 , 3)
(c) (3, – 3, 0)
(d) (1/3, 1/3 ,2)

B

Question. The ratio in which the join of (1, – 2, 3) and (4, 2, – 1) is divided by the xy-plane is
(a) 1 : 3 externally
(b) 3 : 1 internally
(c) 1 : 3 externally
(d) None of thes

B

Question. The point which divides the line joining the points (1, 3, 4) and (4, 3, 1) internally in the ratio 2 : 1, is
(a) (2, – 3, 3)
(b) (2, 3, 3)
(c) 5/2 , 3 , 5/2)
(d) (3, 3, 2)

D

Question. Determine the point in yz-plane which is equidistant from three points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).
(a) (0, 1, 3)
(b) (1, 0, 3)
(c) (0, 2, 3)
(d) (0, 3, 1)

A

Question. What is the locus of a point for which x = 0, z = 0 ?
(a) equation of x-axis
(b) equation of y-axis
(c) equation of z-axis
(d) None of these

B

Question. Let A, B, C be the feet of the perpendicular segments drawn from a point P(3, 4, 5) on the xy, yz and zx – planes, respectively. The distance of the points A, B, C from the point P (in units) respectively are
(a) 5, 2, 4
(b) 3, 4, 5
(c) 5, 3, 4
(d) 3, 5, 4

C

Question. The distance of the point A(2, 3, 4) from the y-axis is
(a) 5 units
(b) √13 units
(c) 5 √2 units
(d) 2 √5 units

D

Question. Let A, B, C be the feet of the perpendicular segments drawn from a point P(3, 4, 5) on the xy, yz and zx-planes, respectively. What are the coordinates of A, B and C ?
(a) (3, 4, 0), (0, 4, 4), (3, 0, 5)
(b) (3, 0, 4), (4, 5, 0), (3, 5, 0)
(c) (3, 5, 0), (0, 5, 4), (0, 3, 4)
(d) (3, 4, 0), (0, 4, 5), (3, 0, 5)

D

Question. If the distance between the points (a, 0, 1) and (0, 1, 2) is √27 , then the value of a is
(a) 5
(b) ±5
(c) –5
(d) None of these

B

Question. The points (1, 2, 3), (– 1, – 1, – 1) and (3, 5, 7) are the vertices of
(a) an equilateral triangle
(b) an isosceles triangle
(c) a right triangle
(d) None of these

D

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. Find the coordinates of L, M and N respectively.
(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)

A

Question. The perpendicular distance of the point (6, 5, 8) from z-axis is
(a) √15 units
(b) √61 units
(c) 8 units
(d) 9 units

B

Question. The distance of the point A(2, 3, 2) from the x-axis is
(a) 5 units
(b) 13 units
(c) 2 5 units
(d) 5 2 units

B

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)

D

Question. In the given figure, if P is (2, 4, 5), then find the coordinates of F. 1
(a) (2, 4, 5)
(b) (4, 0, 5)
(c) (2, 0, 5)
(d) (4, 2, 5)

C

Assertion & Reasoning Based Questions :

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The distance between the points (1 + 11, 0, 0) and (1, –2, 3) is 2 6 units.
Reason : Distance between any two points A(x1, y1, z1) and B(x2, y2, z2) is, |AB|= √(x1+x2)2 + (y2+y1)2 + (z2+z1)2

C

Question. Assertion : The points A(1, –1, 3), B(2, –4, 5) and C(5, –13, 11) are collinear.
Reason : If AB + BC = AC, then A, B, C are collinear.

A

Question. Assertion : The foot of perpendicular drawn from the point A(1, 2, 8) on the xy-plane is (1, 2, 0).
Reason : Equation of xy-plane is y = 0.

C

Question. Assertion : The points A(3, –1, 2), B(1, 2, – 4), C(–1, 1, 2) and D(1, –2, 8) are the vertices of a parallelogram.
Reason : Coordinates of mid-point of a line joining the points A(x1, y1, z1) and B(x2, y2, z2) is (x1+x2/2 , y1+y2/2 , z1+z2/2)

A

Question. Assertion : Coordinates of centroid of a triangle formed by the vertices A(3, 2, 0), B(5, 3, 2) and C(0, 2, 4) is (8/3 , 8/3 ,8/3)
Reason : Coordinates of centroid of a triangle with vertices A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) is (x1+x2+x3/3 , y1+y2+y3/3 , z1+z2+z3/3).