Practice Test 5 ( Vector Product )

Vector Practice Test 5 ( Vector Product )

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1 / 21

If two vectors A and B are perpendicular and have magnitudes 4 and 6 respectively, what is the magnitude of A × B?

A) 0

B) 10

C) 24

D) 12

2 / 21

Given vectors A = 2i + 3j + k and B = i - j + 4k, what is the vector A × B?

A) 14i + 7j - 7k

B) 13i - 7j - 5k

C) 11i + 10j + 1k

D) 0

3 / 21

The direction of the vector A × B is given by:

A) Left-hand rule

B) Right-hand rule

C) Vector addition rule

D) None of the above

4 / 21

If A × B = 0, which of the following must be true?

A) A and B are perpendicular

B) A and B are parallel or one vector is zero

C) Angle between A and B is 90°

D) Vectors have equal magnitudes

5 / 21

What is the magnitude of the cross product A × B when A = 5 units, B = 3 units, and the angle between them is 90°?

A) 15

B) 8

C) 0

D) 2

6 / 21

The cross product of two vectors A and B is:

A) A scalar quantity

B) A vector perpendicular to both A and B

C) A vector parallel to A

D) Zero vector always

7 / 21

If A = 1î + 2ĵ + 3k̂ and B = 2î + 4ĵ + 6k̂, then A × B = ?

A) 0

B) (–3î + 6ĵ – 3k̂)

C) (3î – 6ĵ + 3k̂)

D) (1î + 2ĵ + 3k̂)

8 / 21

The vector product î × k̂ equals:

A) î

B) –ĵ

C) ĵ

D) k̂

9 / 21

If |A| = 5, |B| = 7 and the angle between A and B is 90°, then |A × B| = ?

A) 35

B) 12

C) 0

D) √74

10 / 21

If the angle between vectors A and B is θ, the value of the product
(B × A) · A is equal to:

A) zero

B) BA²sin θcos θ

C) BA² cos θ

D) BA² sin θ

11 / 21

What is the torque of a force F = (2î – 3ĵ + 4k̂) newton acting at a point r = (3î + 2ĵ + 3k̂) metre about the origin?
(Given: τ = r × F)

A) 6î – 6ĵ + 12k̂

B) 17î – 6ĵ – 13k̂

C) –6î + 6ĵ – 12k̂

D) –17î + 6ĵ – 13k̂

12 / 21

The value of the unit vector which is perpendicular to both
A = î + 2ĵ + 3k̂ and
B = î – 2ĵ – 3k̂
is equal to:

A) (î + 2ĵ + 3k̂) / 6

B) (6ĵ – 4k̂) / √52

C) (6ĵ + 4k̂) / √52

D) (2î – ĵ) / √5

13 / 21

The angle between vectors ( A x B ) & (B X A )

A) Zero

B) π

C) π/4

D) π/2

14 / 21

Given are two vectors, A = (2î – 5ĵ + 2k̂) and B = (4î – 10ĵ + ck̂).
What should be the value of c so that vector A and B become parallel to each other?

A) 1

B) 2

C) 3

D) 4

15 / 21

Which of the following option is not true, if vector A = 3î + 4ĵ and B = 6î + 8ĵ, where A and B are magnitudes of A and B?

A) A × B = 0

B) A/B=1/2

C) A . B = 48

D) A=5

16 / 21

The scalar and vector product of two vectors, a = (3î – 4ĵ + 5k̂) and b = (–2î + ĵ – 3k̂) is equal to:

A) –25 & (7î – ĵ – 5k̂)

B) 25 & (–7î + ĵ – 5k̂)

C) 0 & (–7î + ĵ + 3k̂)

D) –25 & (–7î + ĵ + 5k̂)

17 / 21

If we have two vectors A and B and |A| ≠ |B| and |A × B| = |A · B|, then:

A) A & B are perpendicular

B) A & B are parallel

C) A and B are anti-parallel

D) A is inclined to B at an angle of 45°

18 / 21

If two vectors a = 2î + ĵ and b = 3î + 2ĵ, then |a × b| = ?

A) 1

B) √65

C) 8

D) 4

19 / 21

The linear velocity of a rotating body is given by
v = ω × r, where ω is the angular velocity and r is the radius vector.
If ω = î − 2ĵ + 2k̂ and r = 4ĵ − 3k̂ then the value of |v| will be:

A) √29 units

B) 31 units

C) √37 units

D) √41 units

20 / 21

A and B are two vectors and θ is the angle between them. If
|A × B| = √3 (A · B),
then the value of θ will be:

A) 60°

B) 45°

C) 30°

D) 90°

21 / 21

If for two vectors A and B, A × B = 0, then the vectors:

A) are perpendicular to each other.

B) are parallel to each other.

C) act at an angle of 60°.

D) act at an angle of 30°.

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