Introduction To Three Dimensional Geometry Class 11 MCQ and Answers

These Introduction To Three Dimensional Geometry Class 11 MCQ and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Introduction To Three Dimensional Geometry Class 11 MCQ and Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

Introduction To Three Dimensional Geometry Class 11 MCQ

1. The ratio in which the line joining the points(1,2,3) and (-3,4,-5) is divided by the XY-plane is

(A) 2 : 5

(B) 3 : 5

(C) 5 : 2

(D) 5 :3

Answer: 3 : 5


2. The dirction cosines of a line equally inclined to three mutually perpendicular lines having DCs as l1 ,m1 , n1 ,  l2 ,m2 , n2 , l3 ,m3 , n3 are

(A) l1 + l2 , l3 ,  m1 + m2 + m3 , n1 + n2 + n3

(B) (l1 + l2 , l3 )/3,  (m1 + m2 + m3 )/3 , (n1 + n2 + n)/3

(C) (l1 + l2 , l3 )/√3,  (m1 + m2 + m3 )/√3 , (n1 + n2 + n)/√3

(D) None of these

Answer: (l1 + l2 , l3 )/√3,  (m1 + m2 + m3 )/√3 , (n1 + n2 + n)/√3


3. The points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a

(A) Rectangle

(B) Square

(C) Rhombus

(D) None of these

Answer: Square


4. The equation of plane containing the line of intersection of the plane x + y + z – 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1) is

(A) 20x + 23y + 26z + 69 = 0

(B) 20x + 23y – 26z – 69 = 0

(C) 20x – 23y + 26z – 69 = 0

(D) 20x + 23y + 26z – 69 = 0

Answer: 20x + 23y + 26z – 69 = 0


5. There is one and only one sphere through

(A) 4 points not in the same plane

(B) 4 points not lie in the same straight line

(C) none of these

(D) 3 points not lie in the same line

Answer: 4 points not in the same plane


6. The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is

(A) (-3, 5, 2)

(B) (3, 5, 2)

(C) (3, -5, 2)

(D) (3, 5, -2)

Answer: (-3, 5, 2)


7. If the end points of a diagonal of a square are (1, -2, 3) and (2, -3, 5) then the length of the side of square is

(A) √3 unit

(B) 2√3 unit

(C) 3√3 unit

(D) 4√3 unit

Answer: √3 unit


8. If P(x, y, z) is a point on the line segment joining Q(2, 2, 4) and R(3, 5, 6) such that the projections of OP on the axes are 13/5, 19/5, 26/5 respectively, then P divides QR in the ration

(A) 1 : 2

(B) 3 : 2

(C) 2 : 3

(D) 1 : 3

Answer: 3 : 2


9. The coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the YZ plane is

(A) (0, 17/2, 13/2)

(B) (0, -17/2, -13/2)

(C) (0, 17/2, -13/2)

(D) None of these

Answer: (0, 17/2, -13/2)


10. If α, β, γ are the angles made by a half ray of a line respectively with positive directions of X-axis Y-axis and Z-axis, then sin² α + sin² β + sin² γ =

(A) 1

(B) 0

(C) -1

(D) None of these

Answer: None of these


11. The plane 2x – (1 + a)y + 3az = 0 passes through the intersection of the planes

(A) 2x – y = 0 and y + 3z = 0

(B) 2x – y = 0 and y – 3z = 0

(C) 2x + 3z = 0 and y = 0

(D) 2x – 3z = 0 and y = 0

Answer: 2x – 3z = 0 and y = 0


12. The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is

(A) (-3, 5, 2)

(B) (3, 5, 2)

(C) (3, -5, 2)

(D) (3, 5, -2)

Answer: (-3, 5, 2)


13. The equation of plane passing through the point i + j + k and parallel to the plane r . (2i – j + 2k) = 5 is

(A) r . (2i – j + 2k) = 2

(B) r . (2i – j + 2k) = 3

(C) r . (2i – j + 2k) = 4

(D) r . (2i – j + 2k) = 5

Answer: r . (2i – j + 2k) = 3


14. L is the foot of the perpendicular drawn from a point (3, 4, 5) on x-axis. The coordinates of L are

(A) (3,0,0)

(B) (0,4,0)

(C) (0, 0, 5)

(D) none of these

Answer: (3,0,0)


15. 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 these

Answer: none of these


16. If a parallelepiped 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 parallelepiped is

(A) 2√3

(B) 3√

(C) √2

(D) √3

Answer: 2√3


17. The locus of a point for which x = 0 is

(A) xy-plane

(B) yz-plane

(C) zx-plane

(D) None of these

Answer: yz-plane


18. The locus of a point for which y = 0, z = 0 is

(A) equation of x-axis

(B) equation of y-axis

(C) equation at z-axis

(D) none of these

Answer: equation of x-axis


19. A plane is parallel to yz-plane so it is perpendicular to

(A) x-axis

(B) y-axis

(C) z-axis

(D) none of these

Answer: x-axis


20. The point (-2, -3, -4) lies in the

(A) First octant

(B) Seventh octant

(C) Second octant

(D) Eighth octant

Answer: Seventh octant


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