Vector Practice Test 1 ( Addition & Resolution of Vector )

Vector Practice Test 1 ( Addition and Resolution of Vector )

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1 / 38

Unit vector along the vector 4î + 3ĵ is _____

A) (4î + 3ĵ)/5

B) 4î + 3ĵ

C) (4î + 3ĵ)/6

D) (4î + 3ĵ)/10

2 / 38

When two vectors in the same direction are added, the magnitude of resulting vector is equal to _______

A) Sum of magnitudes of the vectors

B) Difference of magnitudes of the vectors

C) Product of magnitudes of the vectors

D) Sum of the roots of magnitudes of the vectors

3 / 38

Following sets of three forces act on a body. Whose resultant cannot be zero

A) 10, 10, 20

B) 10, 20, 23

C) 10, 20, 40

D) 10, 10, 10

4 / 38

When subtracting B = 4î + 2ĵ from A = î – 6ĵ, the resultant A – B is:

A) –3î – 8ĵ

B) 5î + 4ĵ

C) –3î + 8ĵ

D) 3î – 8ĵ

5 / 38

If u and v are perpendicular unit vectors, then |u – v| equals:

A) 0

B) 1

C) √2

D) 2

6 / 38

A plane flies 300 km due north and then 400 km due west. Its resultant displacement is:

A) 500 km northwest

B) 700 km

C) 100 km

D) 250 km

7 / 38

Two vectors of equal magnitude V with angle 60° to each other. The magnitude of their resultant is:

A) V

B) V√2

C) V√3

D) 2V sin 30°

8 / 38

If A = 7î + 24ĵ, the magnitude of A is:

A) 17

B) 25

C) 31

D) 49

9 / 38

Two equal forces $P$ each act at a point with an angle of 120° between them. The magnitude of their resultant is:

A) P

B) 0

C) P/√2

D) P√2

10 / 38

If the sum of two unit vectors is a unit vector, then the magnitude of their difference and the angle between them are, respectively:

A) √2, 60°

B) √3, 60°

C) √2, 120°

D) √3, 120°

11 / 38

At what angle should the two force vectors 5 N and 12 N be added to get a resultant of 13 N?

A) 0°

B) 30°

C) 90°

D) 180°

12 / 38

Two equal forces act at right angles on a point. The magnitude of their resultant is:

A) F

B) 2F

C) F/√2

D) F√2

13 / 38

A particle moves 5 m east then 12 m north. Its resultant displacement from the start is:

A) 13 m

B) 7 m

C) 17 m

D) 6 m

14 / 38

The angle between vector Q and the resultant of (2Q + 2P) and (2Q – 2P)

A) tan⁻¹(P/Q)

B) 0°

C) tan⁻¹((2Q–2P)/(2Q+2P))

D) tan⁻¹(2Q/P)

15 / 38

Two perpendicular forces have magnitudes A and A/2. The magnitude of their resultant is:

A) 5A/2

B) (√5 A)/4

C) (A√5 )/2

D) (A²√5)/2

16 / 38

When A = 2î + 3ĵ + 2k̂ is subtracted from B, the result is 2ĵ. The magnitude of B is:

A) 3

B) √33

C) √6

D) √5

17 / 38

A vector in the xy-plane makes an angle of 30° with the y-axis. Its y-component is 2√3. The magnitude of its x-component is:

A) √3

B) 2

C) 6

D) 1/√3

18 / 38

Given A = (2, 3) and B = (–2, –3), the graphical sum A + B forms:

A) A triangle

B) A straight line

C) A closed loop

D) A parallelogram

19 / 38

Which property of vector addition states A + B = B + A?

A) Associative

B) Commutative

C) Distributive

D) Identity

20 / 38

Which is not part of adding vectors by rectangular components?

A) Resolve each vector into î and ĵ

B) Sum corresponding components

C) Draw the resultant by the parallelogram law

D) Multiply x- and y-components together

21 / 38

Two vectors A and B add to a resultant purely along the x-axis if:

A) Aᵧ + Bᵧ = 0

B) Aₓ + Bₓ = 0

C) Aᵧ = Bᵧ = 0

D) Aₓ and Bₓ are both positive

22 / 38

If A = 8î + 6ĵ and B = –8î + 6ĵ, the resultant A + B lies:

A) along +y-axis

B) along +x-axis

C) in the 1st quadrant

D) in the 2nd quadrant

23 / 38

Which method adds two vectors by drawing them from the same origin to form a parallelogram?

A) Triangle law

B) Parallelogram law

C) Pythagorean law

D) Commutative law

24 / 38

A = 4î + 3ĵ and B = –2î + 6ĵ. What is the angle θ of R from the +x-axis?

A) tan⁻¹(3/4)

B) tan⁻¹(9/2)

C) tan⁻¹(2/9)

D) tan⁻¹(3/6)

25 / 38

A = 3î – 4ĵ, B = –5î + 2ĵ. The resultant A + B is:

A) –2î – 2ĵ

B) –2î + 6ĵ

C) 8î – 2ĵ

D) 2î – 2ĵ

26 / 38

If A_x+ B_x= 0 but A_y + B_y ≠ 0, then A + B

A) lies along the x-axis

B) lies along the y-axis

C) is zero

D) is undefined

27 / 38

Two equal-magnitude vectors at right angles are added. The resultant’s magnitude is V√2 because

A) you multiply one component by √2

B) the dot product equals zero

C) Pythagoras’ theorem on the two equal legs

D) vectors become scalar when perpendicular

28 / 38

A = 5î + 0ĵ and B = 0î + 12ĵ. The magnitude of A + B is

A) 7

B) 13

C) 17

D) 60

29 / 38

Subtracting 2î + 7ĵ from î + ĵ gives ______

A) -î – 6ĵ

B) 3î + 8ĵ

C) î + 6

D) 7ĵ

30 / 38

ding 2î + 7ĵ and î + ĵ gives ______

A) 3î + 8ĵ

B) î + 35ĵ

C) î + 8ĵ

D) 2î + 7ĵ

31 / 38

On adding two vectors we get _____

A) A vector

B) A scalar

C) A number

D) An operation

32 / 38

If u·v = 0 (and neither u nor v is the zero vector), then u and v are:

A) Parallel

B) Perpendicular

C) Equal in length

D) One must be the zero vector

33 / 38

The vector from P(1, 2, 3) to Q(4, 0, 5) is:

A) 3i – 2j + 2k

B) – 3i + 2j – 2k

C) i + j + k

D) 4i + 0j + 5k

34 / 38

A unit vector u satisfies u×i = j. Then u is:

A) k

B) –k

C) j

D) –j

35 / 38

If u and v are two perpendicular unit vectors, then |u + v| equals:

A) 1

B) √2

C) 2

D) 0

36 / 38

Which property holds for any unit vector u?

A) u·u = 1

B) |u| = u

C) u×u = u

D) u + u = 1

37 / 38

The unit vector parallel to a = 3 i – 4 j + 12 k is:

A) (3/13) i – (4/13) j + (12/13) k

B) (3/5) i – (4/5) j + (12/5) k

C) (3/13) i + (4/13) j + (12/13) k

D) (–3/13) i + (4/13) j – (12/13) k

38 / 38

Which of the following is a unit vector?

A) i + j + k

B) ( i + j + k ) / √3

C) 2 i + 0 j + 0 k

D) i – k

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