Practice Test 4 ( Scalar Product )

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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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1	Muhammad Asim Mehsood	3 minutes 9 seconds	35
2	Barakna Zia	4 minutes 8 seconds	35
3	Hilal Riffat	4 minutes 20 seconds	35
4	Sajjadullah	5 minutes 56 seconds	35
5	Shakir Ali Akmal	9 minutes 26 seconds	35
6	amir hamza	13 minutes 34 seconds	35
7	Nosheen hayat	17 minutes 58 seconds	35
8	MAK	18 minutes 59 seconds	35
9	Fatima	20 minutes 8 seconds	35
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11	Kadmore khan	44 minutes 19 seconds	35
12	Mahnoor Sher	48 minutes 24 seconds	35
13	Anum khan	2 minutes 51 seconds	34
14	Bakhtshan khan sher	4 minutes 44 seconds	34
15	Nabiha Saeed	4 minutes 55 seconds	34
16	Sudais Hassan	9 minutes 17 seconds	34
17	Mudasir Rafiq	1 hours 12 minutes 54 seconds	34
18	maimoona	6 minutes 44 seconds	33
19	Muhammad shabib khan	7 minutes 12 seconds	33
20	Shawal khan	24 minutes 33 seconds	33
21	Salwa	39 minutes 56 seconds	33
22	Rahman Ali	1 hours 18 minutes 14 seconds	33
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24	Javeria Karim .	29 minutes 8 seconds	32
25	Fawad khan	1 hours 5 minutes 5 seconds	32
26	Muhammad Yar	9 minutes 45 seconds	31
27	Sayeda Muqaddas Miftah	12 minutes	31
28	Pretty	19 minutes 51 seconds	31
29	Lailma shah	50 minutes 4 seconds	31
30	Doctor	51 minutes 24 seconds	31
31	Dr Dilan	56 minutes 14 seconds	31
32	Malik Muhammad Yasir	1 hours 7 minutes 44 seconds	31
33	Dua Aleem	12 minutes 21 seconds	30
34	Maryam	16 minutes 45 seconds	30
35	Shumaila khan	20 minutes 23 seconds	30
36	Sumaira	28 minutes 16 seconds	30
37	Ayesha	33 minutes 54 seconds	30
38	Haya Khan	40 minutes 27 seconds	30
39	Abdullah	41 minutes 36 seconds	30
40	Ahmad khan	41 minutes 58 seconds	30
41	Shuja	42 minutes 34 seconds	30
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45	Muhammad Salman	1 hours 24 minutes 58 seconds	30
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55	Sabeela Khan	19 minutes 29 seconds	28
56	Owais khan	21 minutes 51 seconds	28
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61	Ajwa Khan	33 minutes 47 seconds	28
62	Muhammad	44 minutes 33 seconds	28
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76	Yashfa	45 minutes 28 seconds	27
77	Hira Niaz	1 hours 5 minutes 19 seconds	27
78	Hanzala Umar	1 hours 18 minutes 10 seconds	27
79	WASIF	1 hours 36 minutes 30 seconds	27
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81	Saman Hassan	3 hours 25 minutes 9 seconds	27
82	Amna Khan	18 minutes 36 seconds	26
83	Raheel Ahmad	18 minutes 50 seconds	26
84	M	24 minutes 20 seconds	26
85	Laiba	27 minutes 59 seconds	26
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87	Eiman Khattak	34 minutes 6 seconds	26
88	HAMAS ALI	39 minutes 41 seconds	26
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96	Ayesha zafar	30 minutes 48 seconds	25
97	Zainab israr	35 minutes 50 seconds	25
98	Maryam	40 minutes 9 seconds	25
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110	..	46 minutes 28 seconds	24
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129	zaidullah	8 minutes 25 seconds	13

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