Match List I with List II. List I List II (a) C → - A → - B → = 0 (i) (b) A → - C → - B → = 0 (ii) (c) B → - A → - C → = 0 (iii) (d) A → + B → = - C → (iv) Choose the correct answer from the options given below:

(a) → (iv), (b) → (iii), (c) → (i), (d) → (ii)

(a) → ( iv ) , (b) → ( i ) , (c) → ( iii ) , (d) → (ii)

(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)

(a) → (i), (b) → (iv), (c) → (ii), (d) → (iii)

Assertion A : If A , B , C , D are four points on a semi-circular arc with a centre at O such that | A B → | = | B C → | = | C D → | . Then, A B → + A C → + A D → = 4 A O → + O B → + O C → Reason R : Polygon law of vector addition yields A B → + B C → + C D → + A D → = 4 A O → In the light of the above statements, choose the most appropriate answer from the options given below.

Both A and R are correct but R is not the correct explanation of A .

A is correct but R is not correct.

A is not correct but R is correct.

Both A and R are correct and R is the correct explanation of A .

The magnitude of vectors OA → , OB → and OC → in the given figure are equal. The direction of OA → + OB → - OC → with x - axis will be:

tan − 1 ⁡ ( 1 − 3 − 2 ) ( 1 + 3 + 2 )

tan − 1 ⁡ ( 3 − 1 + 2 ) ( 1 + 3 − 2 )

tan − 1 ⁡ ( 3 − 1 + 2 ) ( 1 − 3 + 2 )

tan − 1 ⁡ ( 1 + 3 − 2 ) ( 1 − 3 − 2 )

Statement I: If three forces F → 1 , F → 2 and F → 3 are represented by three sides of a triangle and F 1 → + F 2 → = - F → 3 , then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II: A triangle made up of three forces F 1 → , F 2 → and F 3 → as its sides were taken in the same order, satisfies the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:

Both Statement I and Statement II are true.

Statement I is true but Statement II is false.

Both Statement I and Statement II are false.

Statement I is false but Statement II is true.

EASY

Earn 100

Which of the following is a Vector Quantity?

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Important Questions on Physics

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

Vector

A

has a magnitude of

10

units and makes an angle of

30 °

with the positive x-axis. Vector

B

has a magnitude of

20

units and makes an angle of

30 °

with the negative x-axis. What is the magnitude of the resultant between these two vectors?

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

Two vectors

\vec{A}

and

\vec{B}

have equal magnitudes. The magnitude of

(\vec{A} + \vec{B})

n

times the magnitude of

(\vec{A} - \vec{B})

. The angle between

\vec{A}

and

\vec{B}

is:

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

The unit vector

(a \hat{i} + b \hat{j})

is perpendicular to

(\hat{i} + \hat{j}) .

The value of

b

can be:

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

The unit vector perpendicular to the plane of

\vec{A} = \hat{i} - 3 \hat{j} - \hat{k}

and

\vec{B} = 2 \hat{i} + \hat{j} - \vec{k}

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

A vector

\vec{A}

is rotated by a small angle

∆ θ

radians

(∆ θ ≪ 1)

to get a new vector

\vec{B}

. In that case

|\vec{B} - \vec{A}|

is :

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

Consider a frame that is made up of two thin massless rods $A B$ and $A C$ as shown in the figure. A vertical force $\vec{P}$ of magnitude $100 N$ is applied at point $A$ of the frame.

Question Image

Suppose the force is $\vec{P}$ resolved parallel to the arms $A B$ and $A C$ of the frame. The magnitude of the resolved component along the arm $A C$ is $x N$ . The value of $x$ , to the nearest integer, is ________.

[Given : $\sin (35 °) = 0.573, \cos (35 °) = 0.819, \sin (110 °) = 0.939, \cos (110 °) = - 0.342$ ]

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

\vec{A} = 3 \hat{i} - 2 \hat{j} + \hat{k}, \vec{B} = \hat{i} - 3 \hat{ȷ} + 5 \hat{k}

and

\vec{C} = 2 \hat{i} + \hat{j} - 4 \hat{k}

form a right angled triangle then out of the following which one is satisfied?

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

Match List I with List II.

List I		List II
(a)	$\vec{C} - \vec{A} - \vec{B} = 0$	(i)
(b)	$\vec{A} - \vec{C} - \vec{B} = 0$	(ii)
(c)	$\vec{B} - \vec{A} - \vec{C} = 0$	(iii)
(d)	$\vec{A} + \vec{B} = - \vec{C}$	(iv)

Choose the correct answer from the options given below:

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

Resultant of two vectors

\vec{P}

and

\vec{Q}

is of magnitude

R_{1} .

If direction of

\vec{Q}

is reversed, the resultant is of magnitude

R_{2}

. The value of

(R_{1}^{2} + R_{2}^{2})

[\cos (π - θ) = - \cos θ]

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

\vec{A}

and

\vec{B}

are two non-zero vectors inclined at an angle

θ

\hat{a}

and

\hat{b}

are unit vectors along

\vec{A}

and

\vec{B}

respectively. The component of

\vec{A}

in the direction of

\vec{B}

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

The angle between two vectors

x

and

y

θ

. If the resultant vector

z

makes an angle

\frac{θ}{2}

with

x

, then which of the following is true?

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

Two forces

P

and

Q

, of magnitude

2 F

and

3 F

, respectively, are at an angle

θ

with each other. If the force

Q

is doubled, then their resultant also gets doubled. Then, the angle

θ

is:

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

Two vectors

\vec{P}

and

\vec{Q}

have equal magnitudes. If the magnitude of

\vec{P} + \vec{Q}

n

times the magnitude of

\vec{P} - \vec{Q},

then angle between

\vec{P}

and

\vec{Q}

HARD

General Awareness>General Science>Physics>Electricity and Magnetism

In an octagon $A B C D E F G H$ of equal side, what is the sum of $\vec{A B} + \vec{A C} + \vec{A D} + \vec{A E} + \vec{A F} + \vec{A G} + \vec{A H},$ if, $\vec{AO} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$

Question Image

HARD

General Awareness>General Science>Physics>Electricity and Magnetism

$Assertion A :$ If $A, B, C, D$ are four points on a semi-circular arc with a centre at $O$ such that $| \vec{A B} | = | \vec{B C} | = | \vec{C D} | .$ Then, $\vec{A B} + \vec{A C} + \vec{A D} = 4 \vec{A O} + \vec{O B} + \vec{O C}$

$Reason R :$ Polygon law of vector addition yields $\vec{A B} + \vec{B C} + \vec{C D} + \vec{A D} = 4 \vec{A O}$

Question Image

In the light of the above statements, choose the most appropriate answer from the options given below.

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

The magnitude of vectors $\vec{OA}, \vec{OB}$ and $\vec{OC}$ in the given figure are equal. The direction of $\vec{OA} + \vec{OB} - \vec{OC}$ with $x -$ axis will be:

Question Image

MEDIUM

General Awareness>General Science>Physics>Electricity and Magnetism

Statement I: If three forces

{\vec{F}}_{1}, {\vec{F}}_{2}

and

{\vec{F}}_{3}

are represented by three sides of a triangle and

\vec{F_{1}} + \vec{F_{2}} = - {\vec{F}}_{3},

then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement II: A triangle made up of three forces

\vec{F_{1}}, \vec{F_{2}}

and

\vec{F_{3}}

as its sides were taken in the same order, satisfies the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

Figure shows three forces ${\vec{F}}_{1}, {\vec{F}}_{2}$ and ${\vec{F}}_{3}$ acting along the sides of an equilateral triangle. If the total torque acting at point $O$ (centre of the triangle) is zero then the magnitude of ${\vec{F}}_{3}$ is

Question Image

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

Vector

\vec{a} = \hat{i} + 2 \hat{j} + 2 \hat{k}

and

\vec{b} = \hat{i} - \hat{j} + \hat{k}

. What is the unit vector along

\vec{a} + \vec{b}

EASY

General Awareness>General Science>Physics>Electricity and Magnetism

Force

\vec{F}

applied on a body is written as

\vec{F} = (\hat{n} \times \vec{F}) \cdot \hat{n} + \vec{G}

, where

\hat{n}

is a unit vector. The vector

\vec{G}

is equal to

Which of the following is a Vector Quantity?

Important Questions on Physics

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