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 .

EASY

Earn 100

The maximum and minimum magnitudes of the resultant of two forces are $16 N$ and $4 N$ . Calculate the magnitude of individual forces.

Important Questions on Motion in a Plane

EASY

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

MEDIUM

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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:

HARD

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

MEDIUM

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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 :

EASY

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

\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}

MEDIUM

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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?

EASY

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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:

EASY

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

\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?

MEDIUM

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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}

EASY

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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}

MEDIUM

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

The angle between vector $(\vec{A})$ and $(\vec{A} - \vec{B})$ is :

Question Image

HARD

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

$Assertion A :$ 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.

EASY

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

The unit vector

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

is perpendicular to

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

The value of

b

can be:

MEDIUM

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

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

Physics>Mechanics>Motion in a Plane>Scalars and Vectors

The angle, between

\vec{A}

and the resultant of

2 \vec{A} + 3 \vec{B}

and

4 \vec{A} - 3 \vec{B}

The maximum and minimum magnitudes of the resultant of two forces are 16 N and 4 N. Calculate the magnitude of individual forces.

Important Questions on Motion in a Plane

Learn and Prepare for any exam you want !

The maximum and minimum magnitudes of the resultant of two forces are $16 N$ and $4 N$ . Calculate the magnitude of individual forces.