Vectors MCQs

01Which of the following is a vector quantity?
(A) Speed    (B) Displacement    (C) Temperature    (D) Mass
02Which of the following is a scalar quantity?
(A) Velocity    (B) Time    (C) Force    (D) Acceleration
03The magnitude of vector **v** = 3i + 4j is:
(A) 7    (B) 5    (C) 5    (D) √7
04If **a** = 2i – 3j and **b** = i + j, then **a + b** =:
(A) 3i – 2j    (B) 3i – 2j    (C) i – 4j    (D) i + 4j
05What is the negative of vector **u** = 5i – 2j?
(A) 2i – 5j    (B) –5i – 2j    (C) –5i + 2j    (D) 5i + 2j
06Two vectors are orthogonal if their dot product is:
(A) 1    (B) –1    (C) 0    (D) undefined
07Dot product of **a** = 2i + 3j and **b** = i – j is:
(A) 2 – 3 = –1    (B) 2 – 3 = -1    (C) 2 + 3 = 5    (D) 4
08If |**v**| = 4 and **v** is along i, then **v** equals:
(A) 4j    (B) 4k    (C) 4i    (D) –4i
09The unit vector in the direction of **u** = 3i + 4j is:
(A) (3/25)i + (4/25)j    (B) (3/4)i + (4/5)j    (C) (3/5)i + (4/5)j    (D) (5/3)i + (5/4)j
10If vector **p** = 6i + 8j, its magnitude is:
(A) 10    (B) 10    (C) √1000    (D) 14
11Two vectors are collinear if one is a _____ of the other.
(A) sum    (B) dot product    (C) cross product    (D) scalar multiple
12Which rule is used to add two vectors graphically?
(A) Pythagorean rule    (B) Triangle rule / Parallelogram rule    (C) Cosine rule    (D) Sine rule
13If **a** = 4i and **b** = –2i, then resultant **a + b** =:
(A) 2i    (B) 2i    (C) –6i    (D) 8i
14Which of the following is the zero vector?
(A) 0i + 0j    (B) 0i + 0j    (C) i    (D) j
15The position vector of point (2, 3) is:
(A) i + 2j    (B) 3i + 2j    (C) 2i + 3j    (D) 2j + 3i
16If **a** = i + 2j and **b** = 2i + 4j, then **b** is a _____ of **a**.
(A) perpendicular    (B) addition    (C) scalar multiple    (D) unrelated
17Angle between vectors **i** and **j** is:
(A) 0°    (B) 45°    (C) 90°    (D) 180°
18Projection of vector **a** on **b** is given by:
(A) (a·b) **b**    (B) ((a·b)/|b|²) b    (C) a × b    (D) a + b
19Which of the following is true for unit vectors i, j in 2D?
(A) i·j = 1    (B) |i| = |j| = 0    (C) i·j = 0    (D) i = j
20If **a** = 3i – 4j, find a unit vector in the direction of –**a**.
(A) (3/5)i – (4/5)j    (B) –(3/5)i + (4/5)j    (C) –(3/5)i + (4/5)j    (D) (3/5)i + (4/5)j
21If vector from A(1,2) to B(4,6) is **AB**, then **AB** =:
(A) 3i + 4j    (B) 3i + 4j    (C) 1i + 2j    (D) 4i + 6j
22If **u** = 2i + 0j and **v** = 0i + 3j, then **u · v** =:
(A) 6    (B) –6    (C) 0    (D) 5
23Which vector has magnitude √13?
(A) 2i + 2j    (B) 3i + 2j    (C) 3i + 2j    (D) 1i + 3j
24The resultant of two equal vectors at right angles of magnitude a is:
(A) a    (B) √2 a    (C) √2 a    (D) 2a
25If **a** = 5i and **b** = 12j, then |**a + b**| =:
(A) 13    (B) 13    (C) √119    (D) 17
26Which of the following pairs are parallel?
(A) i + j and i – j    (B) 2i + 3j and 3i + 2j    (C) 2i + 4j and i + 2j    (D) i and j
27Vector **a** = 4i + 3j, vector **b** = 8i + 6j. **b** is equal to _____ **a**.
(A) 1/2    (B) 2 ×    (C) –2 ×    (D) not a multiple
28The scalar component of **a** = 3i + 4j on j is:
(A) 3    (B) 4    (C) 5    (D) 7
29Which of the following expresses vector equality? **a = b** means:
(A) same magnitude only    (B) same direction only    (C) same magnitude and direction    (D) same components but opposite sign
30If **a**·**a** = 25, then |**a**| =:
(A) 5    (B) 5    (C) –5    (D) 25
31Which vector is perpendicular to 2i + 3j?
(A) 2i + 3j    (B) 1i + 1j    (C) 3i – 2j    (D) 4i + 6j
32Area of parallelogram formed by vectors **a** and **b** in 2D equals the magnitude of:
(A) a + b    (B) a · b    (C) a × b (in 3D sense)    (D) a – b
33If **a** = i + j and **b** = i – j, then |a × b| (treating as 3D vectors with k=0) =:
(A) 0    (B) 2    (C) 2    (D) √2
34Which statement is true: a unit vector has magnitude ______.
(A) 0    (B) 2    (C) 1    (D) depends on direction
35If **v** = 7i – 24j, what is |v|?
(A) 25    (B) 25    (C) √625    (D) 17
36Midpoint of points P(1,1) and Q(5,3) has position vector:
(A) 3i + 2j    (B) 3i + 2j    (C) 6i + 4j    (D) 2i + 1j
37Displacement from A(2,5) to B(–1,1) is:
(A) –3i – 4j    (B) –3i – 4j    (C) 3i + 4j    (D) 1i + 4j
38Which gives the vector equal to 0 when added to 4i – 7j?
(A) 4i – 7j    (B) –4i + 7j    (C) –4i + 7j    (D) 0
39If resultant of **a** and **b** is zero, then **b** =:
(A) **a**    (B) orthogonal to a    (C) –**a**    (D) 2**a**
40Angle between vectors 3i + 4j and 4i + 3j is (use dot product):
(A) 0°    (B) 90°    (C) cos⁻¹(24/25)    (D) 45°
41Vector components of 5 units at 60° to positive x-axis are:
(A) (5cos60)i + (5sin60)j    (B) (2.5)i + (4.330)j    (C) (5)i + (0)j    (D) (0)i + (5)j
42Which of the following is NOT a property of vector addition?
(A) Commutative    (B) Associative    (C) Distributive over vector cross product)    (D) Existence of zero vector
43Scalar multiplication 3(2i – j) equals:
(A) 6i – 3j    (B) 6i – 3j    (C) 2i – 3j    (D) 6i + 3j
44If **a** and **b** are perpendicular and |a| = 3, |b| = 4 then |a + b| =:
(A) 1    (B) 5    (C) 5    (D) √7
45The vector from origin to point (–3, 4) is:
(A) –3i – 4j    (B) 3i – 4j    (C) –3i + 4j    (D) 4i – 3j
46Which of the following describes the direction cosines of a unit vector making angle 90° with x-axis and 0° with y-axis?
(A) (1,0,0)    (B) (0,1,0)    (C) (0,1,0)    (D) (0,0,1)
47If **a** = 2i + 3j and scalar ฮป = 0, then ฮปa =:
(A) 2i + 3j    (B) 0i + 0j    (C) 0    (D) not defined
48The component of vector 7i + 24j along i is:
(A) 7    (B) 7    (C) 24    (D) 25
49Which of these vectors is equal to 2i + 3j – i + j?
(A) i + 2j    (B) i + 4j    (C) 3i + 2j    (D) i – 2j
50Two vectors of magnitudes 6 and 8 have resultant of magnitude 10. The angle between them is:
(A) 60°    (B) 120°    (C) 90°)    (D) 45°