Vector Algebra
1) What is the value of a × b?
- 6
- -3
- -9
- -6
2) What is the value of a. b and hence find the value of θ?
- 102.4°
- 100.3°
- 101.1°
- 104.3°
3) Use the dot product to find the size of angle θ?
- 16.4°
- 106.8°
- 66.8°
- 59.8°
4) If k is any positive number, what is the size of the angle between the vectors a = (k, k) and b = (-3, 4)?
- 91.9°
- 56.5°
- 101.1°
- 81.9°
5) Which one of the following is not a unit vector?
a. (0,1,0) b. (0,0,1) c. (1/√3,1/√3,1/√3 ) d. (1,1,1)
- b
- d
- a
- c
6) What is the size of the angle between the vectors a = (2, 5, -1) and b = (-3, 2, 6)?
- 99.0
- 96.0
- 98.0
- 93.0
7) Vector a has magnitude 3, vector b has magnitude 4, the angle between a and b is 30° and n is the unit vector at right angles to both a and b. What is a × b?
- 2n
- 4n
- 6n
- 5n
8) Vector a has magnitude 3√2, vector b has magnitude 5. The angle between a and b is 135° and n is the unit vector at right angles to both a and b. What is the value of a × b?
- 13n
- 16n
- 12n
- 15n
9) Vector a has magnitude 1/√3, vector b has magnitude 4, the angle between a and b is 60° and n is the unit vector at right angles to both a and b. What is the value of a × b?
- 4n
- 3n
- 6n
- 2n
10) What is the cross product of a = (1, 2, 3) and b = (4, 5, 6)?
- (8, 6, 7)
- (-3, -6, 3)
- (3, 9, 3)
- (-3, 6, -3)
11) What is the cross product of a = (-2, 3, 5) and b = (-4, 1, -6)?
- (-29, -72, 30)
- (-53, -72, 10)
- (-23, -32, 10)
- (-33, -32, 40)
12) What is the cross product of a = (2, -5, 1) and b = (3, -2, -4)?
- (22, 11, 11)
- (25, 16, 11)
- (25, 13, 14)
- (28, 12, 11)
13) If a = (-2, 1, 1), b = (2, 1, 1) and c = a × b, what is the magnitude of c?
- 7√2
- 5√3
- 9√2
- 4√2
14) If a = (2, 0, 1), b = (0, 1, 1/2) and c = a × b, what is the magnitude of c?
- √6
- √5
- √8
- √3
15) If a = (2, -4, 4), b = (4, 0, 3) and c = a × b, what is the magnitude of c?
- 18√5
- 9√5
- 10√5
- 12√5
16) a, b and c are three vectors such that c is perpendicular to both a and b. What is the value of a × b × c?
- (0, 1, 0)
- (0, 0, 0)
- (0, 0, 1)
- (1, 0, 0)
17) What should be added in vector to get its resultant a unit vector i, if a = 3i + 4j - 2k
- -2i + 4j + 2k
- -i – j + k
- -2i – 4j + 2k
- -2i – 4j + 5k
18) The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is
- 15
- 12
- 13
- 10
19) The position vectors of two points A and B are i + j - k and 2i - j + k respectively. Then |AB| = ?
- 6
- 4
- 0
- 8
20) If a and b are two non-zero and non-collinear vectors, then a + b and a - b are?
- Linearly independent
- Linearly spanning
- Linearly dependent
- None of these
21) Find the angle between two vectors a and b having the same length √2, and their scalar product is -1
- 2π/3
- 2π
- π/3
- π
22) Let a and b be two vectors of the same magnitude, such that the angle between them is 60° a × b = 8. Find
- 2
- 1
- 5
- 4
23) If vector a = 5i - j - 3k and vector b = i + 3j - 5k, then the vectors (a + b) × (a - b) is
- Non parallel
- Perpendicular
- Collinear
- Parallel
24) Find
- -i - j - 2k
- -i - j + 2k
- -2i - 3j - 2k
- i + j + 2k
25) Find the magnitude of
- √19
- 91
- 19
- √91
26) If a and b are two vectors such that
- 7
- 5
- 4
- 3
27) Find the values of x for which vectors a = 2x²i + 4xj + k and 7i - 2j + xk is obtuse.
- 0 < x < -1
- 0 < x < -1/2
- 0 < x < 1/2
- 0 > x > 1/2
28) Find the projection of vector 7i + j - 4k on vector 2i +6j + 3k
- 7/8
- 9/7
- 16/7
- 8/7
29) Here which of the following represents the linear combination of vectors?
- Both 1 and 2
- Both 1 and 3
- None of these
- Only 1
30) The magnitude of a vector F is 10 units and the direction of the vector is 60° with the horizontal. Find the components of the vector?
- (5, 5√3)
- (4, 4√2)
- (6, 6√3)
- (9, 9√2)