Practice Test 4 ( Scalar Product )

Vector Practice Test 4 ( Scalar Product )

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1 / 35

The angle which the vector A = 2i + 3j makes with the y-axis, where i and j are unit vectors along x- and y-axis, respectively, is:

A) cos⁻¹(3/5)

B) cos⁻¹(2/3)

C) tan⁻¹(2/3)

D) sin⁻¹(2/3)

2 / 35

The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:

A) are not equal to each other in magnitude.

B) cannot be predicted.

C) are equal to each other.

D) are equal to each other in magnitude.

3 / 35

A and B are two vectors given by A = 2i + 3j and B = i + j. The component of A parallel to B is:

A) (2i − j)

B) (5/2)(i − j)

C) (5/2)(i + j)

D) (3i − 2j)/2

4 / 35

The magnitude of the resultant of two vectors of magnitude 3 units and 4 units is 1 unit. What is the value of their dot product?

A) -12 units

B) -7 units

C) -1 units

D) 0

5 / 35

If A = 2i + j − k, B = i + 2j + 3k, and C = 6i − 2j − 6k, then the angle between (A + B) and C will be:

A) 30°

B) 45°

C) 60°

D) 90°

6 / 35

The angle between the two vectors (–2i + 3j + k) and (i + 2j – 4k) is:

A) 0°

B) 90°

C) 180°

D) 45°

7 / 35

A particle moves from position null to (11i + 11j + 15k) due to a uniform force of (4i + j + 3k) N. If the displacement is in m, then the work done will be:

A) 100 J

B) 200 J

C) 300 J

D) 250 J

8 / 35

If A = aî + bĵ + ck̂ and A · A = 49, then which of the following is true?

A) a + b + c = 7

B) a² + b² + c² = 49

C) a – b + c = 0

D) 3

9 / 35

. If |A| = 5, |B| = 12, and A · B = 30, then the angle between A and B is:

A) 0°

B) 60°

C) 90°

D) 120°

10 / 35

If the scalar projection of vector A on vector B is maximum, then angle between them is:

A) 0°

B) 45°

C) 90°

D) 180°

11 / 35

Let vector A = aî + bĵ. The angle between A and the x-axis is 60°. Then the value of b/a is:

A) √3

B) 1/√3

C) 1

D) 0

12 / 35

Let A = 2î – 3ĵ + k̂, B = –î + 4ĵ + 2k̂. Find A · B.

A) 1

B) –4

C) –3

D) -12

13 / 35

If vector A = xî + 3ĵ and vector B = 2î + yĵ, and A · B = 0, then the relation between x and y is:

A) xy = –6

B) 2x + 3y = 0

C) x = y

D) x + y = 0

14 / 35

If angle between two vectors is acute, then their dot product is:

A) Zero

B) Negative

C) Positive

D) Depends on magnitude only

15 / 35

If A · B = 0 and |A| = 3, |B| = 4, the angle between A and B is:

A) 0°

B) 45°

C) 90°

D) 180°

16 / 35

For any vectors A and B, (A + B) · (A + B) equals:

A) |A|² + |B|²

B) (A · B)²

C) |A|² + |B|² + 2(A · B)

D) |A – B|²

17 / 35

Let a = 2î + ĵ – k̂, b = î – 3ĵ + k̂, and c = î + ĵ + k̂. If a · (b + λc) = 0, then λ = ?

A) 0

B) 1

C) -1

D) 2

18 / 35

The value of (A + B) · (A – B) is:

A) |A|² + |B|²

B) |A|² – |B|²

C) 2(A · B)

D) |A + B| · |A – B|

19 / 35

If A · B = A · C and A ≠ 0, then

A) B = C

B) B – C is perpendicular to A

C) B = –C

D) A is perpendicular to B + C

20 / 35

If A = aî + bĵ and B = bî – aĵ, then A · B is:

A) 0

B) a² + b²

C) a² – b²

D) 2ab

21 / 35

If the dot product of two vectors is negative, the angle between them lies between:

A) 0° – 90°

B) 90° – 180°

C) 0° – 45°

D) 45° – 90°

22 / 35

If A = 3i + 4j and B = 4i – 3j, find the angle between them using scalar product.

A) 90°

B) 180°

C) 45°

D) 0°

23 / 35

Two vectors A and B satisfy A·B = |A||B|. The angle between them is:

A) 0°

B) 45°

C) 90°

D) 180°

24 / 35

If the angle between two vectors is obtuse (>90°), then their dot product is:

A) Positive

B) Zero

C) Negative

D) Undefined

25 / 35

The scalar product of two non-zero vectors is zero. Which of the following must be true?

A) Vectors are collinear

B) Vectors are equal in magnitude

C) Vectors are perpendicular

D) Vectors lie in different planes

26 / 35

What is the scalar product of two vectors inclined at 120°, both having magnitude 10?

A) 100

B) -50

C) 50

D) -100

27 / 35

Which of the following statements is incorrect about scalar product?

A) It depends on the angle between vectors

B) It gives a scalar result

C) It is non-commutative

D) It is distributive

28 / 35

If |A| = 5, |B| = 10, and angle between them is 60°, then A·B = ?

A) 50

B) 25

C) 100

D) 75

29 / 35

The scalar product of vector A with itself is:

A) A

B) 1

C) |A|

D) |A|²

30 / 35

Which of the following is true about scalar product?

A) Commutative: A·B = B·A

B) Distributive: A·(B + C) = A·B + A·C

C) A·A = |A|²

D) All of the above

31 / 35

The scalar product of two unit vectors is 1. The angle between them is:

A) 0°

B) 45°

C) 90°

D) 180°

32 / 35

If A·B = 0 and neither A nor B is zero, then:

A) A and B are parallel

B) A and B are anti-parallel

C) A and B are perpendicular

D) Angle between them is 0°

33 / 35

What is the scalar product of vector A = 2i + 3j and B = -i + 4j?

A) 10

B) 2

C) 6

D) 4

34 / 35

The scalar (dot) product of two vectors is a:

A) Vector

B) Scalar

C) Tensor

D) Complex number

35 / 35

If two vectors are perpendicular, then their scalar product is:

A) Maximum

B) Minimum

C) Zero

D) One

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