MCQs on Vectors & 3D Geometry

This test covers Vector Algebra and Three-Dimensional Geometry as prescribed in NCERT Class 12.

1. 1. A vector has:

      (A) only magnitude

      (B) only direction

      (C) magnitude and direction

      (D) neither magnitude nor direction

   2. Which of the following is a scalar quantity?

      (A) Velocity

      (B) Displacement

      (C) Force

      (D) Mass

   3. The magnitude of a zero vector is:

      (A) 1

      (B) −1

      (C) 0

      (D) undefined

   4. If →a = 2i − j + 2k, then |→a| equals:

      (A) 3

      (B) √9

      (C) √(9)

      (D) 3

   5. The unit vector along x-axis is:

      (A) i

      (B) j

      (C) k

      (D) 0

   6. Vector addition is:

      (A) commutative

      (B) associative

      (C) both A and B

      (D) neither

   7. →a − →b equals:

      (A) →b − →a

      (B) →a + (−→b)

      (C) →a + →b

      (D) →b + (−→a)

   8. The dot product of two perpendicular vectors is:

      (A) 1

      (B) maximum

      (C) minimum

      (D) 0

   9. →a · →a equals:

      (A) |a|

      (B) |a|²

      (C) 0

      (D) 1

   10. The cross product of parallel vectors is:

       (A) 1

       (B) maximum

       (C) zero

       (D) undefined

   11. →a × →b is:

       (A) scalar

       (B) vector

       (C) zero always

       (D) undefined

   12. The direction of →a × →b is given by:

       (A) left-hand rule

       (B) right-hand thumb rule

       (C) Fleming’s rule

       (D) screw rule only

   13. Direction cosines satisfy:

       (A) l + m + n = 1

       (B) l² + m² + n² = 1

       (C) lmn = 1

       (D) l²m²n² = 1

   14. Direction ratios of a line are:

       (A) unique

       (B) always positive

       (C) not unique

       (D) zero

   15. If direction ratios are (2, −2, 1), direction cosines are:

       (A) (2,−2,1)

       (B) (2/3, −2/3, 1/3)

       (C) (1/3,2/3,2/3)

       (D) (−2/3,2/3,1/3)

1. 1. The distance between two identical points is:

      (A) 1

      (B) 0

      (C) −1

      (D) undefined

   2. The distance of point (x,y,z) from origin is:

      (A) x+y+z

      (B) √(x²+y²+z²)

      (C) x²+y²+z²

      (D) |x+y+z|

   3. The vector equation of a line is:

      (A) ax+by+cz=d

      (B) →r = →a + λ→b

      (C) y = mx + c

      (D) x/a = y/b

   4. The symmetric form of a line is:

      (A) →r = →a + λ→b

      (B) ax+by+cz=d

      (C) (x−x₁)/a = (y−y₁)/b = (z−z₁)/c

      (D) x²+y²+z²=0

   5. The angle between two lines depends on:

      (A) their position

      (B) their length

      (C) their direction ratios

      (D) their intercepts

   6. If cosθ = 0, the lines are:

      (A) parallel

      (B) intersecting

      (C) perpendicular

      (D) coincident

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