Introduction To Three Dimensional Geometry Class 11 Questions and Answers

These Introduction To Three Dimensional Geometry Class 11 Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Introduction To Three Dimensional Geometry Class 11 Questions 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 Questions

1. The coordinate of foot of perpendicular drawn from the point A(1, 0, 3) to the join of the point B(4, 7, 1) and C(3, 5, 3) are

(A) (5/3, 7/3, 17/3)

(B) (5, 7, 17)

(C) (5/3, -7/3, 17/3)

(D) (5/7, -7/3, -17/3)

Answer: (5/3, 7/3, 17/3)


2. A vector r is equally inclined with the coordinate axes. If the tip of r is in the positive octant and |r| = 6, then r is

(A) 2√3(i – j + k)

(B) 2√3(-i + j + k)

(C) 2√3(i + j – k)

(D) 2√3(i + j + k)

Answer: 2√3(i + j + k)


3. The locus of a point which moves so that the difference of the squares of its distances from two given points is constant, is a

(A) Straight line

(B) Plane

(C) Sphere

(D) None of these

Answer: Plane


4. The maximum distance between points (3sin θ, 0, 0) and (4cos θ, 0, 0) is

(A) 3

(B) 4

(C) 5

(D) Can not be find

Answer: 5


5. The angle between the vectors with direction ratios are 4, -3, 5 and 3, 4, 5 is

(A) π/2

(B) π/3

(C) π/4

(D) π/6

Answer: π/3


6. If the equation of a plane is lx + my + nz = p is in the normal form, then which is not true

(A) l, m and n are the direction cosines of the normal to the plane

(B) p is the length of the perpendicular from the origin to the plane

(C) The plane passes through the origin for all values of p

(D) l2 + m2 + n2 = 1

Answer: The plane passes through the origin for all values of p


7. The angle between the planes r . n1 = d1 and r . n2 = d2 is

(A) cos θ ={|n1 | * |n2 |}/ (n1 . n2 )

(B) cos θ = (n1 . n2 )/{|n1 | * |n2 |}2

(C) cos θ = (n1 . n2 )/{|n1 | * |n2 |}

(D) cos θ = (n1 . n2 )2 /{|n1 | * |n2 |}

Answer: cos θ = (n1 . n2 )/{|n1 | * |n2 |}


8. The centroid of ∆ ABC is at (1, 1, 1). If coordinates of A and B are (3, -5, 7) and (-1, 7, -6) respectively then the coordinates of point C is

(A) (1, -1, 2)

(B) (1, 1, -2)

(C) (1, 1, 2)

(D) (-1, 1, 2)

Answer: (1, 1, 2)


9. If the points A(1, 0, –6), B(–5, 9, 6) and C(–3, p, q) are collinear, then the value of p and q are

(A) -6 and -2

(B) -6 and 2

(C) 6 and -2

(D) 6 and 2

Answer: 6 and 2


10. The distance of point P(3,4, 5) from the yz-plane is

(A) 3 units

(B) 4 units

(C) 5 units

(D) 550

Answer: 3 units


11. Under what condition does the equation x2 + y2 + z2 + 2ux + 2vy + 2wz + d represent a real sphere

(A) u2 + v2 + w2 = d2

(B) u2 + v2 + w2 > d

(C) u2 + v2 + w2 < d

(D) u2 + v2 + w2 < d2

Answer: u2 + v2 + w2 > d


12. The coordinate of foot of perpendicular drawn from the point A(1, 0, 3) to the join of the point B(4, 7, 1) and C(3, 5, 3) are

(A) (5/3, 7/3, 17/3)

(B) (5, 7, 17)

(C) (5/3, -7/3, 17/3)

(D) (5/7, -7/3, -17/3)

Answer: (5/3, 7/3, 17/3)


13. Three planes x + y = 0 , y + z = 0 , and x + z = 0

(A) none of these

(B) meet in a line

(C) meet in a unique point

(D) meet taken two at a time in parallel lines

Answer: meet in a unique point


14. The locus of a point which moves so that the difference of the squares of its distances from two given points is constant, is a

(A) Straight line

(B) Plane

(C) Sphere

(D) None of these

Answer: Plane


15. 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)


16. 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)


17. The projections of a directed line segment on the coordinate axes are 12, 4, 3. The DCS of the line are

(A) 12/13, -4/13, 3/13

(B) -12/13, -4/13, 3/13

(C) 12/13, 4/13, 3/13

(D) None of these

Answer: 12/13, 4/13, 3/13


18. 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


19. The vector equation of a sphere having centre at origin and radius 5 is

(A) |r| = 5

(B) |r| = 25

(C) |r| = √5

(D) none of these

Answer: |r| = 5


20. A parallelepiped is formed by planes drawn through the points (2,3,5) and (5,9,7), parallel to the coordinate plane. The length of a diagonal of the parallelopiped is

(A) 7

(B) √38

(C) √155

(D) none of these

Answer: 7


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