Vector Algebra for Competitive Exam Success

Vector Algebra

Scalar Product Vector Product Vectors in 2D & 3D

Q. If A = 5i + 12j and B = 12i - 5j, what is the scalar product A · B?

A. 0
B. 60
C. 70
D. 80

Solution

A · B = (5)(12) + (12)(-5) = 60 - 60 = 0.

Correct Answer: B — 60

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Q. If A = 5i + 12j and B = 3i + 4j, find A · B.

A. 63
B. 60
C. 64
D. 65

Solution

A · B = (5)(3) + (12)(4) = 15 + 48 = 63.

Correct Answer: A — 63

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Q. If A = 5i + 2j + 3k and B = 1i - 4j + 2k, find A · B.

A. -1
B. 0
C. 1
D. 2

Solution

A · B = (5)(1) + (2)(-4) + (3)(2) = 5 - 8 + 6 = 3.

Correct Answer: B — 0

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Q. If A = 5i + 2j + 3k and B = 4i - j + 2k, find the scalar product A · B.

A. 26
B. 28
C. 30
D. 24

Solution

A · B = (5)(4) + (2)(-1) + (3)(2) = 20 - 2 + 6 = 24.

Correct Answer: B — 28

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Q. If A = 5i + 2j + 3k and B = 4i - j + 6k, find A · B. (2020)

A. 38
B. 32
C. 30
D. 28

Solution

A · B = (5)(4) + (2)(-1) + (3)(6) = 20 - 2 + 18 = 36.

Correct Answer: B — 32

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Q. If A = 5i + 2j and B = 3i + 6j, find the angle θ between A and B if A · B = |A||B|cos(θ).

A. 60°
B. 45°
C. 30°
D. 90°

Solution

A · B = 5*3 + 2*6 = 15 + 12 = 27. |A| = √(5^2 + 2^2) = √29, |B| = √(3^2 + 6^2) = √45. cos(θ) = 27/(√29 * √45). θ = 45°.

Correct Answer: B — 45°

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Q. If A = 5i + 2j and B = 3i - 4j, find A · B.

A. -1
B. 7
C. 1
D. 0

Solution

A · B = (5)(3) + (2)(-4) = 15 - 8 = 7.

Correct Answer: A — -1

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Q. If A = 5i + 5j and B = 5i - 5j, what is the value of A · B?

A. 0
B. 25
C. 50
D. 10

Solution

A · B = (5)(5) + (5)(-5) = 25 - 25 = 0.

Correct Answer: B — 25

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Q. If A = 5i - 2j + k and B = 3i + 4j - 2k, calculate A · B.

A. -1
B. 1
C. 0
D. 2

Solution

A · B = (5)(3) + (-2)(4) + (1)(-2) = 15 - 8 - 2 = 5.

Correct Answer: A — -1

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Q. If A = 5i - 2j and B = -3i + 4j, calculate A · B. (2023)

A. -23
B. -7
C. 7
D. 23

Solution

A · B = (5)(-3) + (-2)(4) = -15 - 8 = -23

Correct Answer: A — -23

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Q. If A = 5i - 2j and B = -3i + 4j, what is the value of A · B?

A. -23
B. -7
C. 7
D. 23

Solution

A · B = (5)(-3) + (-2)(4) = -15 - 8 = -23.

Correct Answer: A — -23

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Q. If A = 6i + 8j and B = 2i + 3j, calculate A · B.

A. 36
B. 42
C. 38
D. 30

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 36

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Q. If A = 6i + 8j and B = 2i + 3j, find A · B.

A. 36
B. 42
C. 30
D. 24

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 36

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Q. If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.

A. 42
B. 54
C. 48
D. 36

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: C — 48

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Q. If A = 6i + 8j and B = 2i + 3j, what is the scalar product A · B?

A. 42
B. 36
C. 30
D. 48

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: B — 36

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Q. If A = 6i + 8j and B = 2i + 3j, what is the value of A · B?

A. 54
B. 60
C. 48
D. 42

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 54

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Q. If A = 6i + 8j and B = 3i + 4j, what is the angle between A and B?

A. 0°
B. 30°
C. 45°
D. 90°

Solution

A · B = 6*3 + 8*4 = 18 + 32 = 50. |A| = 10, |B| = 5. cos(θ) = 50/(10*5) = 1. θ = 0°.

Correct Answer: D — 90°

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Q. If A = 6i + 8j and B = 3i + 4j, what is the value of A · B?

A. 50
B. 54
C. 48
D. 52

Solution

A · B = (6)(3) + (8)(4) = 18 + 32 = 50.

Correct Answer: C — 48

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Q. If A = 6i - 2j and B = -3i + 4j, find A · B.

A. -18
B. -24
C. -12
D. -6

Solution

A · B = (6)(-3) + (-2)(4) = -18 - 8 = -26.

Correct Answer: A — -18

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Q. If A = 7i + 1j and B = 1i + 7j, calculate A · B.

A. 56
B. 58
C. 60
D. 62

Solution

A · B = (7)(1) + (1)(7) = 7 + 7 = 14.

Correct Answer: A — 56

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Q. If A = 7i + 1j and B = 1i + 7j, find A · B.

A. 56
B. 14
C. 8
D. 50

Solution

A · B = (7)(1) + (1)(7) = 7 + 7 = 14.

Correct Answer: A — 56

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Q. If A = 7i + 1j and B = 2i + 3j, what is the scalar product A · B? (2022)

A. 23
B. 21
C. 19
D. 17

Solution

A · B = (7)(2) + (1)(3) = 14 + 3 = 17

Correct Answer: A — 23

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Q. If A = 7i - 2j and B = -3i + 4j, find A · B. (2021)

A. -26
B. -28
C. -30
D. -32

Solution

A · B = (7)(-3) + (-2)(4) = -21 - 8 = -29.

Correct Answer: A — -26

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Q. If A = 7i - 3j and B = -2i + 5j, what is the value of A · B?

A. -29
B. -31
C. -25
D. -27

Solution

A · B = (7)(-2) + (-3)(5) = -14 - 15 = -29.

Correct Answer: A — -29

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Q. If A = ai + bj and B = ci + dj, what is the expression for A · B?

A. ac + bd
B. ab + cd
C. ad + bc
D. a + b + c + d

Solution

A · B = (ai + bj) · (ci + dj) = ac + bd.

Correct Answer: A — ac + bd

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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is the value of A · B?

A. 32
B. 30
C. 28
D. 26

Solution

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

Correct Answer: B — 30

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Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)

A. 25
B. 30
C. 35
D. 50

Solution

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25

Correct Answer: B — 30

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Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is A · B?

A. 25
B. 30
C. 35
D. 20

Solution

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25.

Correct Answer: B — 30

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Q. If the angle between two vectors A and B is 90 degrees, what is A · B?

A. 0
B. 1
C. 2
D. 3

Solution

A · B = |A||B|cos(90°) = |A||B| * 0 = 0.

Correct Answer: A — 0

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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the distance from the origin to point P?

A. 5
B. 6
C. 7
D. 8

Solution

Distance = |r| = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29.

Correct Answer: B — 6

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Vector Algebra

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