Practice Test 5 ( Vector Product )

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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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Pos.	Name	Duration	Points
1	Abdul Saboor orakzai	47 seconds	21
2	Nabiha Saeed	1 minutes 18 seconds	21
3	Hilal Riffat	2 minutes	21
4	Muhammad Asim Mehsood	2 minutes 4 seconds	21
5	Ayesha akbar	2 minutes 32 seconds	21
6	Sajjadullah	3 minutes 1 seconds	21
7	Malik Muhammad Yasir	6 minutes 29 seconds	21
8	Nosheen hayat	7 minutes 57 seconds	21
9	Ayesha Bibi	12 minutes 9 seconds	21
10	Fatima	18 minutes 38 seconds	21
11	Salwa	22 minutes 26 seconds	21
12	Laik	30 minutes 47 seconds	21
13	chand	30 minutes 58 seconds	21
14	Kaleem Ullah	47 minutes 51 seconds	21
15	Anum khan	1 minutes 16 seconds	20
16	Muhammad shabib khan	1 minutes 22 seconds	20
17	Hammad wahid	7 minutes 43 seconds	20
18	HASHAM ZEB	23 minutes 59 seconds	20
19	Ahmad khan	25 minutes 3 seconds	20
20	areeba	30 minutes 46 seconds	20
21	Haya Khan	38 minutes 21 seconds	20
22	Muhammad Mutarab	39 minutes 16 seconds	20
23	maimoona	1 minutes	19
24	Bakhtshan khan sher	5 minutes 44 seconds	19
25	Barakna Zia	11 minutes 47 seconds	19
26	Saad Ali	20 minutes 38 seconds	19
27	Muhammad Yar	24 minutes 30 seconds	19
28	Lailma shah	29 minutes 4 seconds	19
29	Doctor	39 minutes 3 seconds	19
30	Hayat Ullah	40 minutes 34 seconds	19
31	Muhammad Hammad Ul Hassan	40 minutes 50 seconds	19
32	Faiq Ahmad	42 minutes 42 seconds	19
33	Rahman Ali	1 hours 4 minutes 33 seconds	19
34	Owais khan	3 hours 55 minutes 58 seconds	19
35	Laiba	4 minutes 54 seconds	18
36	Saman Hassan	11 minutes 59 seconds	18
37	Muhammad	13 minutes 35 seconds	18
38	Atique Khan	18 minutes 19 seconds	18
39	Maryam	18 minutes 37 seconds	18
40	Sabeela Khan	21 minutes 43 seconds	18
41	Noor e Adan	25 minutes 11 seconds	18
42	Mahnoor Sher	27 minutes 14 seconds	18
43	Muhammad Salman	28 minutes 52 seconds	18
44	Anonymous Epreparian	29 minutes 4 seconds	18
45	Dr Dilan	30 minutes 29 seconds	18
46	Dr Khan	32 minutes 58 seconds	18
47	Mudasir Rafiq	34 minutes 14 seconds	18
48	Dreamer Zubair 🩺	37 minutes 12 seconds	18
49	Muhammed Hilal Khan	40 minutes 41 seconds	18
50	Muhammad Tariq	44 minutes 9 seconds	18
51	Qazi omama	47 minutes 1 seconds	18
52	Fawad khan	1 hours 7 minutes 42 seconds	18
53	Amna Tahir	7 hours 15 minutes 6 seconds	18
54	kashif	12 minutes 19 seconds	17
55	Abdullah Khan	17 minutes 32 seconds	17
56	Bakhtawar Jadoon	17 minutes 39 seconds	17
57	Ayesha	18 minutes 30 seconds	17
58	Abdullah Shahab	25 minutes 44 seconds	17
59	Fakhir zaman	28 minutes 44 seconds	17
60	amir hamza	32 minutes 5 seconds	17
61	Noor Afshan	32 minutes 54 seconds	17
62	Sardar Ul Mulk	39 minutes 28 seconds	17
63	Muhammad Salman	40 minutes 45 seconds	17
64	Eman Ashfaq	43 minutes	17
65	Afifa Ijaz	1 hours 11 minutes 34 seconds	17
66	zaaraa Toraa	12 minutes 8 seconds	16
67	Junaid iqbal	12 minutes 26 seconds	16
68	Abdullah Gull	19 minutes 51 seconds	16
69	muhammad Mustafa	24 minutes 39 seconds	16
70	..	28 minutes 1 seconds	16
71	Yashfa	29 minutes 6 seconds	16
72	Javeria Karim .	30 minutes 25 seconds	16
73	Ashhad Khan Noon	32 minutes 19 seconds	16
74	zeeshan Ihsan	41 minutes 45 seconds	16
75	Sana	57 minutes 57 seconds	16
76	Naina	1 hours 1 minutes 43 seconds	16
77	Madeeha hussain	18 minutes 38 seconds	15
78	Muhammad Sudais	19 minutes 6 seconds	15
79	Sana hidayat	22 minutes 32 seconds	15
80	Abdullah	23 minutes 26 seconds	15
81	Syed Azlan Shah	26 minutes 29 seconds	15
82	Yamaan Qazi	28 minutes 2 seconds	15
83	Humna	34 minutes 4 seconds	15
84	Fatima	39 minutes 9 seconds	15
85	Muhammad Izhar	39 minutes 13 seconds	15
86	Aiman Saeed	42 minutes 13 seconds	15
87	ASAD ALI	56 minutes 1 seconds	15
88	ZARGHUNA	1 hours 7 minutes 24 seconds	15
89	Muhammad Ashan Zafar	1 hours 16 minutes 24 seconds	15
90	Mahnoor	1 hours 43 minutes 53 seconds	15
91	Amna Khan	14 minutes 24 seconds	14
92	Gul Epreparian	15 minutes 7 seconds	14
93	Bravion	24 minutes 48 seconds	14
94	samra	25 minutes 34 seconds	14
95	Shumaila khan	30 minutes 17 seconds	14
96	Maryam	39 minutes 25 seconds	14
97	Muhammad Safwan	44 minutes 2 seconds	14
98	WASIF	46 minutes 3 seconds	14
99	Diya	47 minutes 10 seconds	14
100	ILLIYIN ALI	53 minutes 40 seconds	14
101	umama arshad	54 minutes 40 seconds	14
102	Muhammad Zakrya	55 minutes 2 seconds	14
103	HAMAS ALI	59 minutes 48 seconds	14
104	Abdullah	4 minutes 15 seconds	13
105	laiba	12 minutes 47 seconds	13
106	Moavia Rashid	18 minutes 17 seconds	13
107	Raheel Ahmad	21 minutes 56 seconds	13
108	a ahmed	23 minutes 40 seconds	13
109	Husna	26 minutes 59 seconds	13
110	Aila noor	33 minutes 45 seconds	13
111	Sumaira	39 minutes 23 seconds	13
112	Burhan khan	40 minutes 13 seconds	13
113	Atta ULLAH	42 minutes 42 seconds	13
114	Sayeda Muqaddas Miftah	1 hours 9 seconds	13
115	Eiman Khattak	1 hours 19 minutes 12 seconds	13
116	Hira Niaz	44 minutes	12
117	Laiba eman	45 minutes 47 seconds	11
118	Farhan Khan	6 minutes 15 seconds	10
119	Arsalan Abbas	11 minutes 10 seconds	10
120	Arooba khan	27 minutes 51 seconds	10
121	SAADi	4 minutes	8
122	zaidullah	5 minutes 19 seconds	5
123	Eprepare Academy	21 seconds	1

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