Vectors(11th And 12th > Physics ) Questions and answers for exam Preparation

11th And 12th > Physics

VECTORS MCQs

Total Questions : 30 | Page 1 of 3 pages

Two vectors of the same physical quantity are unequal if

they have the same magnitude and the same direction
they have different magnitudes but the same direction
they have the same magnitude but different directions
they have different magnitudes and different directions.

Discuss Question

Answer: Option A. -> they have the same magnitude and the same direction
:
B, C, and D
For many purposes, two vectors

⃗ A a n d ⃗ B

may be defined to be equal if they have the same magnitude and point in the same direction.

Question 2.

What happens if a vector is multiplied by a number 2?

The magnitude of the vector is doubled but its direction remains the same
The magnitude of the vector remains the same but its direction is reversed
The magnitude of the vector id doubled and its direction is reversed
Neither the magnitude nor the direction of the vector undergo any change

Discuss Question

Answer: Option A. -> The magnitude of the vector is doubled but its direction remains the same
:
A
Multiplication of a vector by a real positive number n makes its magnitude n times but does not change the direction of the vector.
Hence the correct choice is (a).

Question 3.

The magnitude of the resultant of two vectors of magnitudes 3 units and 4 units in 5 units. What is the angle between two vectors?

$\frac{π}{4}$
$\frac{π}{2}$
$\frac{3 π}{4}$
$π$

Discuss Question

Answer: Option B. ->

\frac{π}{2}

:
B
The magnitude R of the resultant vector R of two vectors A and B inclined at an angle

θ

is given by

R^{2} = A^{2} + B^{2} + 2 A B cos θ

cos θ = \frac{R^{2} - A^{2} - B^{2}}{2 A B} = \frac{(5)^{2} - (3)^{2} - (4)^{2}}{2 \times 3 \times 4} = 0

∴

θ = \frac{π}{2} .

Hence the correct choice is (b)

Question 4.

A null vector has

zero magnitude and a specific direction
a finite magnitude and no specific direction
a finite magnitude and a specific direction
zero magnitude and no specific direction

Discuss Question

Answer: Option D. -> zero magnitude and no specific direction
:
D
If vectors A and B are equal, i.e. A = B, then their difference (A – B) is defined as a null vector. It has a zero magnitude and no specific direction.
Hence the correct choice is (d).

Question 5.

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. The angle between the resultant and either vector will be

$60^{\circ}$
$90^{\circ}$
$120^{\circ}$
$150^{\circ}$

Discuss Question

Answer: Option A. ->

60^{\circ}

:
A
From the triangle law of vector addition, it is clear that the vectors R, A and B must be represented by the three sides of an equilateral triangle because the magnitudes of the three vectors are equal. Hence the angle

α

between vectors R and A is

60^{\circ}

. Alternatively, the value of

α

is given by

tan α = \frac{B sin θ}{A + B cos θ} = \frac{sin θ}{1 + cos θ} (∵ A = B)

= \frac{sin 120^{\circ}}{1 + cos 120^{\circ}} = 1.732

Which gives

α = 60^{\circ} .

Hence the correct choice is (a)

Question 6.

The magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm?

1 cm, 1 cm
1 cm, 3 cm
1 cm, 5 cm
1 cm, 7 cm

Discuss Question

Answer: Option A. -> 1 cm, 1 cm
:
A and D
The magnitude R of the resultant of two vectors A and B depends upon the magnitudes of A and B and the angle

θ

between them and is given by

R^{2} = A^{2} + B^{2} + 2 A B c o s θ

When

θ = 0

, R is maximum given by

R_{m a x}^{2} = A^{2} + B^{2} + 2 A B

or,

R_{m a x} = A + B

When

θ = 180^{0}

, R is minimum given by

R_{m a x}^{2} = A^{2} + B^{2} - 2 A B

or,

R_{m i n} = A - B

Thus, the magnitude of resultant will lie between A – B and A + B.
Hence the correct choices are (a) and (d).

Question 7.

Which of the given 2 vectors are negative of each other?

(E) & (D)
(A) & (D)
both option a & b
None of these

Discuss Question

Answer: Option B. -> (A) & (D)
:
B

From the diagram, both A and D have a magnitude of 2 units and are facing opposite directions.

Question 8.

Given two vectors a vector and b vector where b makes an angle theta with the positive direction of a as shown. Find the magnitude of the resultant according to triangle law in this case.

I tried and i think have the answer in the first attempt.
I am trying but I am stuck
I tried and did not get the answer initially but after a few attempts I think I have the right answer now.
I didn't try and don't want to do it on my own. I want to watch you doing it and spoon feed me like a baby

Discuss Question

Answer: Option C. -> I tried and did not get the answer initially but after a few attempts I think I have the right answer now.
:
C

Question 9.

If the river is flowing to your left, In which general direction must you swim to avoid being eaten by the crocodiles on both the sides?

It doesn't matter how the river is flowing, I can swim straight towards the other bank
I must swim exactly against the river ie. towards the right
I must swim in some direction between left and straight
I must swim somewhere between right and straight

Discuss Question

Answer: Option D. -> I must swim somewhere between right and straight
:
D

You must swim somewhere between right and straight.

Question 10.

Which of the given 2 vectors are same?

(A) & (C)
(C) & (B)
both option (A) & (B)
None of these

Discuss Question

Answer: Option B. -> (C) & (B)
:
B

For 2 vectors to be equal their magnitude and direction has to be same.

Option A: says vector A and E surely they are pointed in the same direction but if we see magnitude wise the vector A has a magnitude of 2 units or it is only 2 boxes long, while vector E has magnitude of 3 units, so vector A & E can't be same.

Option B: says vector C & B, they are surely pointing in the same direction are their magnitudes also same.

Vector C has a unit of $2 \sqrt{2}$ units and so does vector B.

So option B is correct.

Here we conclude that we can translate a vector anywhere on the 3D space, it wouldn't change it as long as I keep the magnitude of the vector same and keep it pointing in the same direction.