Fsc Second Year Math Mcqs Vectors consists of 350+ mcqs. Prepare these mcqs for ECAT, exam and all admission test preparation.
Vector analysis mcqs with answers
1. Two non zero vectors a and b are perpendicular if and only ifA) a . b = 1
B) a . b = 0
C) a × b = 1
D) a × b = 0.
2. Find non negative a if |ai + (a+1)j+2k|=3
A) 0
B) -1
C) 2
D) -2
E) 1
3. Find vector whose magnitude is 4 and parallel to 2i -3j +6k.
A) (8/7, 12/7, 24/7)
B) (- 8/7, 12/7, -24/7)
C) (8/7, -12/7, 24/7)
D) (-8/7, -12/7, -24/7)
4. If u= 2i + 3j +4k, v= -i +3j-k and w= I +6j +zk represents the sides of a triangle. What is value of z?
A) 1
B) 2
C) 3
D) 4
5. i . i =
A) 0
B) 1
C) i
D) j
6. j . k =
A) 0
B) 1
C) i
D) j
7. Which of the following triples can be the direction angles of a single vector.
A) 45° ,45°, 60°
B) 30° ,45°, 60°
C) 45° ,60°, 60°
D) None of these
8. Find PQ if P= (2,1,5) and Q= (1,3,1)
A) (1,2,4)
B) (-1,-2,-4)
C) (1,-2,4)
D) (-1,2,-4)
9. If u= 2i + 3j + k and v= 4i+6j+2k then u+2v is
A) (6,9,3)
B) (10,15,5)
C) (-2,3,-1)
D) (-6,9,3)
10. A vector is said to be unit vector if magnitude of a vector is
A) 0
B) -1
C) 2
D) -2
E) 1
11. Projection of B on A is
A) A.B/A
B) A.B/B
C) A.B/AB
D) A.B
12. Projection of vector u= ai+ bj+ ck along i is
A) a
B) c
C) b
D) a+b
13. The angle between the vectors 2i+ 3j+k and 2i-j-k is
A) ã„«/6
B) ã„«/4
C) ã„«/2
D) ã„«
14. If the vectors 2ai+j-k and i+aj+4k are perpendicular to each other then the value of a is
A) 3
B) 1/3
C) 2/3
D) 4/3
15. k × i =
A) 0
B) j
C) -j
D) 1
16. If A and B are parallel vectors then A × B =
A) 0
B) 1
C) -1
D) 2
17. The work done when the point of application of the force 3i-j moves in a straight line from the point (2,1) to the point (6,3) is
A) 5 units
B) 10 units
C) 15 units
D) 22 units
18. (i-j).(j-k)×(k-j)=
A) 1
B) 0
C) i-k
D) j-k
19. j . k × i =
A) i
B) j
C) 1
D) k
20. [a b c] equals
A) 1
B) 0
C) a
D) b
21. a × b= 0 and a . b= 0 then
A) a and b are parallel
B) a and b are perpendicular
C) either a=0 or b=0
D) both a and b are non zero
22. If A and B are opposite directed then A B=
A) AB
B) -AB
C) ABsinθ
D) ABtanθ
23. i . k equals
A) j
B) i
C) 1
D) 0
24. If A and B have same directed then A B=
A) AB
B) -AB
C) ABsinθ
D) ABtanθ
25. The work done by a force F through a displacement d is
A) Fdsecθ
B) Fdsinθ
C) F.d
D) Fdtanθ
26. A constant force F acting on a body, displaces it from A to B. The work done by F is equal to
A) F.AB
B) F× AB
C) -F× AB
D) -F.AB
27. Name of the angle between two non zero vectors a and b is
A). a . b
B).
C)
D)
A) 0
B) 1
C) 2
D) Not defined
29. Find the value of [k, i, j]
A) 0
B) 1
C) 2
D) 3
30. Find projection of u= 3i+ j- k on v= -2i- j+ k is
A)
B)
C)
D)
31. A . B is
A) vector quantity
B) scalar quantity
C) anti commutative
D) neither vector nor scalar
32. A . B is
A) vector quantity
B) scalar quantity
C) anti commutative
D) neither vector nor scalar
33. Scalar quantity in the following is
A) force
B) displacement
C) velocity
D) temperature
34. The vector quantity in the following is
A) distance
B) temperature
C) energy
D) angular acceleration
35. Unit vector along y axis is
A) i
B) j
C) k
D) none
36. If v is a vector for which v.i=0, v.j=0, v.k=0 then value of v will be
A) 0
B) i
C) j
D) k
37. If a= (2,1,-1), b=(1,-1,1) then a × b is
A) (0,3,3)
B) (0,-3,3)
C) (0,-3,-3)
D) (0,3,-3)
38. Let a= i + j , b= i - j then a × b is
A) -2i
B) -2j
C) -2k
D) -2
39. Unit vector containing a and b where a= (2,-6,-3) and b= (4,3,-1) is
A) 1/7 (3,2,6)
B) 1/7 (3,-2,6)
C) 1/7 (3,2,-6)
D) 1/7 (3,2,6)
40. The volume of parallelpiped for which u= 3i + 2k , v= i + 2j +k, w= -j+ 4k
A) 13
B) 6
C) 17
D) 25
41. Value of 2i ×2j .k is
A) 4
B) 8
C) 9
D) 1
42. Value of 3j . k × i is
A) 1
B) 2
C) 3
D) 4
43. Value of [k i j] is
A) 1
B) 0
C) 2
D) k
44. Value of [i i k] is
A) 1
B) 0
C) 2
D) k
45. u . (v × w) + v . (w × u) + w . (u × v) =
A) 3 u . (v × w)
B) 3 v . (w × u)
C) 3 w . (u × v)
D) None of these
46. Volume of tetrahedron of vertices (2,1,8), (3,2,9), (2,1,4), (3,3,10) is
A) 3/2
B) 2/3
C) 8/3
D) 3/8
47. If the point at which a constant force f is equal to 4 i +3j + 5k is applied to an object moves from P(3,1,-2) to Q(2,4,6). Then work done is
A) 36
B) 45
C) 28
D) 12
48. A force F= 4i - 3k, passes through the point A(2,-2,5). The moment of force F about the point B(1,-3,1) is
A) (3,4,7)
B) (4,-19, 3)
C) (3,-19,4)
D) (-3,19,-4)
49. Sum of the vectors AB and CD of four points A(1,-1), B(2,0), C(-1,3), D(-2,2)
A) 0
B) 1
C) 2
D) 3
50. The vector whose magnitude is 2 and is parallel to -i +j + k is
A) ( 2/√3, 2/√3,2/√3)
B) ( -2/√3, 2/√3,2/√3)
C) ( 2/√3, -2/√3,2/√3)
D) ( 2/√3, 2/√3,-2/√3)
Q.1 The physical quantity which is completely specified by its magnitude only is called
(a) vector
(b) scalar
(c) variable
(d) constant
Q.2 The physical quantity which is completely specified by both its magnitude and direction is called
(a) vector
(b) scalar
(c) variable
(d) constant
Q.3 An example of scalar quantity is
(a) energy
(b) force
(c) velocity
(d) acceleration
Q.4 An example of scalar quantity is
(a) force
(b) work
(c) velocity
(d) acceleration
Q.5 An example of scalar quantity is
(a) acceleration
(b) force
(c) velocity
(d) power
Q.6 The scalar quantity in the following is
(a) acceleration
(b) distance
(c) velocity
(d) force
Q.7 The scalar guantity in the following is
(a) density
(b) displacement
(c) velocity
(d) force
Q.8 The scalar quantity in the following is
(a) displacement
(b) charge
(c) velocity
(d) force
Q.9 The scalar quantity in the following is
(a) speed
(b) torque
(c) velocity
(d) force
Q.10 The scalar quantity in the following is
(a) velocity
(b) displacement
(c) mass
(d) force
Q.11 The scalar quantity in the following is
(a) time
(b) displacement
(c) velocity
(d) force
Q.12 The scalar quantity in the following is
(a) force
(b) displacement
(c) velocity
(d) temperature
(Gujranwala Board, 2005)
Q.13 The scalar quantity in the following is
(a) force
(b) displacement
(c) length
(d) velocity
Q.14 The scalar quantity in the following is
(a) force
(b) acceleration
(c) pressure
(d) velocity
Q.15 An example of scalar quantity is
(a) force
(b) acceleration
(c) weight
(d) calorie
Q.16 An example of scalar quantity is
(a) force
(b) acceleration
(c) weight
(d) kinetic energy
Q.17 An example of scalar quantity is
(a) force
(b) frequency
(c) weight
(d) acceleration
Q.18 An example of vector quantity is
(a) energy
(b) force
(c) work
(d) power
Q.19 An example of vector quantity is
(a) velocity
(b) energy
(c) work
(d) power
Q.20 An example of vector quantity is
(a) work
(b) energy
(c) acceleration
(d) power
Q.21 An example of vector quantity is
(a) distance
(b) displacement
(c) energy
(d) power
Q.22 An example of vector quantity is
(a) distance
(b) power
(c) energy
(d) torque
Q.23 An example of vector quantity is
(a) distance
(b) power
(c) energy
(d) momentum
Q.24 The vector quantity in the following is
excellent job
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