EASY

Earn 100

Given that $\vec{A} + \vec{B} + \vec{C} = 0$ , out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt{2}$ times that of either of two having equal magnitudes. Then, angle between vectors are given by

50% studentsanswered this correctly

Important Questions on Measurements and Motion

MEDIUM

Science>Physics>Measurements and Motion>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:

EASY

Science>Physics>Measurements and Motion>Scalars and Vectors

Group of vector quantities are:

MEDIUM

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>Scalars and Vectors

Let

\vec{u} = 2 \hat{i} + \hat{j}

and

\vec{v} = 3 \hat{i} - 5 \hat{j}

. Consider three points

P, Q

and

R

having the position vectors

(\frac{5}{2}) \hat{i} - 2 \hat{j}, (\frac{7}{3}) \hat{i} - \hat{j}

and

(\frac{9}{4}) \hat{i}

respectively. Among these, the points in the line passing through

\vec{u}

and

\vec{v}

are

EASY

Science>Physics>Measurements and Motion>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}

MEDIUM

Science>Physics>Measurements and Motion>Scalars and Vectors

O A B C

is a tetrahedron. If

D, E

are the midpoints of

O A

and

B C

respectively, then

\vec{D E} =

EASY

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>Scalars and Vectors

The point of intersection of the lines joining points

\hat{i} + 2 \hat{j}, 2 \hat{i} - \hat{j}

and

- \hat{i}, 2 \hat{i}

EASY

Science>Physics>Measurements and Motion>Scalars and Vectors

Find the vector Equation and Cartesian Equation of the sphere whose centre is

(- 1, 0, 1)

and radius is

2

MEDIUM

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>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

EASY

Science>Physics>Measurements and Motion>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

MEDIUM

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>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

Science>Physics>Measurements and Motion>Scalars and Vectors

Work is a vector quantity.

MEDIUM

Science>Physics>Measurements and Motion>Scalars and Vectors

P Q R S T

is a pentagon, then the resultant of forces

\vec{P Q}, \vec{P T}, \vec{Q R}, \vec{S R}, \vec{T S}

and

\vec{P S}

HARD

Science>Physics>Measurements and Motion>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

Given that A→+B→+C→=0, out of three vectors two are equal in magnitude and the magnitude of third vector is 2 times that of either of two having equal magnitudes. Then, angle between vectors are given by

Important Questions on Measurements and Motion

Learn and Prepare for any exam you want !

Given that $\vec{A} + \vec{B} + \vec{C} = 0$ , out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt{2}$ times that of either of two having equal magnitudes. Then, angle between vectors are given by