## NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry MCQ’s with Answers

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## NCERT **Maths MCQs for Class 12 Question and Answers Chapter 10 Vector Algebra PDF**

### Q1. Write the intercept cut off by the plane 2x + y – z = 5 on the x-axis.

Option – For intercept on the x-axis, put y = 0 and z = 0 ⇒ 2x = 5 ⇒ x = 5/2 ∴ x-intercept=5/2

### Q2. The distance of point (2, 5, 7) from the x-axis is

(a) 2

(b) √74

(c) √29

(d) √53

Option b – √74

### Q3. P is a point on the line segment joining the points (3, 5, -1) and (6, 3, -2). If y-coordinate of point P is 2, then its x-coordinate will be

(a) 2

(b)17/3

(c) 15/2

(d) -5

Option c – 15/2

### Q4. A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to

(a) 2

(b) 1

(c) -2

(d) -1

Option d – -1

### Q5. The equations of y-axis in space are

(a) x = 0, y = 0

(b) x = 0, z = 0

(c) y = 0, z = 0

(d) y = 0

Option b -x = 0, z = 0

### Q6. If the direction cosines of a line are ,k/3, k/3, k/3, then value of k is

(a) k > 0

(b) 0 < k < 1.

(c) k =1/3

(d) k = ± 73

Option d – k= -+ 73

### Q7. Distance between planes

Option c – 13/9

### Q8. The line joining the points (0, 5, 4) and (1, 3, 6) meets XY-plane at the point *__* .

*__*

Option – (-2, 9, 0), as line is x-1/1 = y-3/-2 = z-6/2 General point on line is (λ + 1, -2λ + 3, 2λ + 6) If it meets AT-plane, then 2λ + 6 = 0 ⇒ λ = – 3 ∴ Point is (-2, 9, 0)

### Q9. A line makes angles α, β, γ with z-axis, x-axis and y-axis respectively. Then direction cosines of line are cos β, cos γ, cos α. State true or false.

Option – True, as direction cosines of a line are cosines of the angles which a line makes with x, y and z-axes respectively.

### Q10. True, as direction cosines of a line are cosines of the angles which a line makes with x, y and z-axes respectively.

Option – Let angle with z-axis be γ. cos²90° + cos²60° + cos² γ = 1 ⇒ 0 + + cos² γ = 1 ⇒ cos² γ = 3/4 cos γ = +√3/2 γ = 30°, 150°

### Q11. Four points (0, -1, -1) (-4, 4, 4) (4, 5, 1) and (3, 9, 4) are coplanar. Find the equation of the plane containing them.

(a) 5x + 7y + 11z – 4 =0

(b) 5x – 7y + 11z + 4 = 0

(c) 5x – 7y – 11z – 4 = 0

(d) 5x + 7y – 11z + 4 = 0

Option b – 5x – 7y + 11z + 4 = 0

### Q12. Find the equation of plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).

(a) x + 2y = 0

(b) x – y = 2

(c) -x + 2y = 2

(d) x + y = 2

Option d – x + y = 2

### Q13. The vector equation of the plane passing through the origin and the line of intersection of the plane r.a = λ and r.b = µ is

(a) r.(λa – µb) = 0

(b) r.(λb – µa) = 0

(c) r.(λa + µb)= 0

(d) r.(λb + µa) = 0

Option b – r.(λb – µa) = 0

### Q14. The angle between the planes 3x + 2y + z – 5 = 0 and x + y – 2z – 3 = 0 is

Option – c

### Q15. The equation of the plane through the point (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is

(a) 3x + 3y – 2z = 0

(b) x – 2y + z = 2

(c) 2x + y – z = 2

(d) 5x – 3y + 2z = 0

Option c – 2x + y – z = 2

### Q16. The shortest distance between the lines x = y = z and x + 1 – y = z/0 is

(a)1/2

(b)1√3

(c)1√6

(d)1√5

Option c – 1√6

### Q17. The shortest distance between the lines x = y + 2 = 6z – 6 and x + 1 = 2y = -12z is

(a) 1/2

(b) 2

(c) 1

(d) 3/2

Option b – 2

### Q18. The angle between the straight line x-1/2 = y+3/ -1 = z-5/2 and the plane 4x – 2y + 4z = 9 is

(a) 60°

(b) 90°

(c) 45°

(d) 30°

Option b – 90°

### Q19. Distance of the point (α, β, γ) from y-axis is

(a) β

(b) |β|

(c) |β| + |γ|

(d) √α2+√γ2

Option d – √α2+√γ2

### Q20. The reflection of the point (α, β, γ) in the xy-plane is

(a) (α, β, 0)

(b) (0, 0, γ)

(c) (-α, -β, -γ)

(d) (α, β, -y)

Option d – (α, β, -y)

### Q21. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2), is equal to

(a) 9 sq. units

(b) 18 sq. units

(c) 27 sq. units

(d) 81 sq. units

Option a – 9 sq. units

### Q22. The locus represented by xy + yz = 0 is

(a) A pair of perpendicular lines

(b) A pair of parallel lines

(c) A pair of parallel planes

(d) A pair of perpendicular planes

Option d – A pair of perpendicular planes

### Q23. Which of the following is false?

(a) 30°, 45°, 60° can be the direction angles of a line is space.

(b) 90°, 135°, 45° can be the direction angles of a line is space.

(c) 120°, 60°, 45° can be the direction angles of a line in space.

(d) 60°, 45°, 60° can be the direction angles of a line in space.

Option a – 30°, 45°, 60° can be the direction angles of a line is space.

### Q24. If a line makes an angle θ1, θ2, θ3 with the axis respectively, then cos 2θ1 + cos 2θ2 + cos 2θ3 =

(a) -4

(b) -2

(c) -3

(d) -1

Option d – -1

### Q25. The equation of the plane passing through three non- collinear points with position vectors a, b, c is

(a) r.(b × c + c × a + a × b) = 0

(b) r.(b × c + c × a + a × b) = [abc]

(c) r.(a × (b + c)) = [abc]

(d) r.(a + b + c) = 0

Option b – r.(b × c + c × a + a × b) = [abc]