Vectors and Scalars MCQs 20 min Score: 0 Attempted: 0/20 Subscribe 1. Magnitude of the vector 2i – 2j – k is: (A) 4 (B) 3 (C) 2 (D) 1 2. Unit vector of i + j + k is: (A) i + j + k (B) (1/3)(i + j + k) (C) 1/3 (i + j + k) (D) 1/2 (i + j + k) 3. Unit vector of i – 2j – 2k is: (A) i – 2j – 2k (B) 1/3 (i – 2j – 2k) (C) 1/3 (i – 2j – 2k) (D) 1/2 (i – 2j – 2k) 4. If i, j and k are orthogonal unit vectors, then j × i is: (A) k (B) –k (C) 1 (D) –1 5. Magnitude of vector i – 3j + 5k is: (A) 3 (B) 25 (C) 35 (D) √35 6. If l, m and n are direction cosines, then: (A) l² + m² + n² = 1 (B) m² + n² – l² = 1 (C) l + m + n = 1 (D) l² + m² + n² = 0 7. If θ is the angle between vectors a and b, then cosθ is: (A) a·b (B) (a·b)/(|a||b|) (C) (a·b)/|a| (D) (a·b)/|b| 8. If a = a₁i + a₂j + a₃k, b = b₁i + b₂j + b₃k, then a·b is: (A) a₁b₁i + a₂b₂j + a₃b₃k (B) a₁b₁ + a₂b₂ + a₃b₃ (C) a₁b₂ + a₂b₃ + a₃b₁ (D) None of these 9. a·b = 0 implies that a and b are: (A) Perpendicular (B) Parallel (C) Non-parallel (D) Oblique 10. If a = i + j + k and b = i – j – mk are perpendicular then m = (A) 1 (B) –2 (C) ±1 (D) ±3 11. a·b is a: (A) Vector quantity (B) Scalar quantity (C) Unity (D) None of these 12. a·a is equal to: (A) 1 (B) a² (C) a (D) None of these 13. If a = 2i – 3j + k and b = –i + 2j + 7k then a·b is: (A) –1 (B) –2 (C) –3 (D) –4 14. If a × b = 0 then a and b are: (A) Non-parallel (B) Parallel (C) Perpendicular (D) None of these 15. The cross product of two vectors a and b is: (A) ab cosθ (B) ab sinθ (C) ab sinθ n̂ (D) ab cosθ n̂ 16. If n̂ is unit vector in direction of a × b then n̂ = (A) (a × b)/|a||b| (B) (a · b)/|a||b| (C) (a × b)/(|a||b| sinθ) (D) (a × b)/|a × b| 17. a × b is area of: (A) Triangle (B) Rectangle (C) Parallelogram (D) Sector 18. a × b is equal to: (A) –(b × a) (B) b × a (C) a × b (D) b × a (same) 19. If a and b are collinear vectors, then: (A) a × b = 0 (B) a · b = 0 (C) a – b = 0 (D) a + b = 0 20. a × b is a: (A) Vector quantity (B) Scalar quantity (C) Unity (D) None of these
