Three vectors P → , Q → and R → are shown in the figure. Let, S be any point on the vector R → . The distance between the points P and S is b R → . The general relation among vectors P → , Q → and S → are

S → = 1 - b P → + b 2 Q →

S → = 1 - b 2 P → + b Q →

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 .

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.

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)

EASY

Earn 100

When vector $\vec{A} = 2 \hat{i} + 3 \hat{j} + 2 \hat{k}$ is subtracted from vector $\vec{B}$ , it gives a vector equal to $2 \hat{j}$ . Then the magnitude of vector $\vec{B}$ will be:

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Important Questions on Kinematics

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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:

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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>Kinematics>Basics of Motion in a Plane

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?

HARD

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Three vectors

\vec{P}, \vec{Q}

and

\vec{R}

are shown in the figure. Let,

S

be any point on the vector

\vec{R}

. The distance between the points

P

and

S

b |\vec{R}|

. The general relation among vectors

\vec{P}, \vec{Q}

and

\vec{S}

are

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

If the sum of two unit vectors is again a unit vector, then magnitude of their difference is

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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}

HARD

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

$Assertion A :$ 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

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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>Kinematics>Basics of Motion in a Plane

The angle, between

\vec{A}

and the resultant of

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

and

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

HARD

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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>Kinematics>Basics of Motion in a Plane

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>Kinematics>Basics of Motion in a Plane

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?

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

\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

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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>Kinematics>Basics of Motion in a Plane

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

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

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)