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