EASY

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If two vectors $2 \hat{i} + 3 \hat{j} - \hat{k}$ and $- 4 \hat{i} - 6 \hat{j} - λ \hat{k}$ are parallel, then find the value of $λ$ .

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Important Questions on Mathematical Tools in Physics

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

If vectors

\vec{A} = \cos ω t \hat{i} + s i n ω t \hat{j}

and

\vec{B} = c o s \frac{ω t}{2} \hat{i} + \sin \frac{ω t}{2} \hat{j}

are functions of time, then the value of

t

at which they are orthogonal to each other is:

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

\vec{P} = 2 \hat{ı} - 2 \hat{j} + 3 \hat{k}

and

\vec{Q} = \hat{ı} + \hat{j} + 2 \hat{k}

, then cosine of angle between

\vec{P}

and

\vec{Q}

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

\vec{A}

and

\vec{B}

are two vectors satisfying the relation

\vec{A} \cdot \vec{B} = | \vec{A} \times \vec{B} |

. Then the value of

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

will be:

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Three particles

P, Q

and

R

are moving along the vectors

\vec{A} = \hat{i} + \hat{j}, \vec{B} = \hat{j} + \hat{k}

and

\vec{C} = - \hat{i} + \hat{j}

, respectively. They strike on a point and start to move in different directions. Now particle

P

is moving normal to the plane which contains vector

\vec{A}

and

\vec{B} .

Similarly particle

Q

is moving normal to the plane which contains vector

\vec{A}

and

\vec{C} .

The angle between the direction of motion of

P

and

Q

\cos^{- 1} (\frac{1}{\sqrt{x}}) .

Then the value of

x

.

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Let

|\vec{A_{1}}| = 3, |\vec{A_{2}}| = 5

and

|\vec{A_{1}} + \vec{A_{2}}| = 5 .

The value of

(2 \vec{A_{1}} + 3 \vec{A_{2}}) \cdot (3 \vec{A_{1}} - 2 \vec{A_{2}})

is:

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

What will be the projection of vector

\vec{A} = \hat{i} + \hat{j} + \hat{k}

on vector

\vec{B} = \hat{i} + \hat{j} ?

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

A triangular plate is shown. A force $\vec{F} = 4 \hat{i} - 3 \hat{j}$ is applied at point $P .$ The torque at point $P$ with respect to point $O$ and $Q$ are:

Question Image

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}

, then the angle between

\vec{P}

and

\vec{Q}

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

HARD

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

In a triangle

A B C

, the sides

A B

and

A C

are represented by the vectors

3 \hat{i} + \hat{j} + \hat{k}

and

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

respectively. Calculate the angle

∠ A B C .

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Find the angle between the two vectors:

\vec{a} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k}

\vec{b} = 5 \hat{i} + 3 \hat{j} + \hat{k}

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

The vectors

2 r \hat{i} + 3 r \hat{j} + 4 r \hat{k}, a r \hat{i} + b r \hat{j} + c r \hat{k}

are normal to each other only if

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Two vectors

\vec{X}

and

\vec{Y}

have equal magnitude. The magnitude of

(\vec{X} - \vec{Y})

n

times the magnitude of

(\vec{X} + \vec{Y})

. The angle between

\vec{X}

and

\vec{Y}

is :

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Two vectors have magnitude

3

and

5

. If the angle between them is

60 °

, then the dot product of two vectors will be

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

\vec{A}

is a vector quantity such that

|\vec{A}| =

non-zero constant. Which of the following expression is true for

\vec{A}

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Which of the following relations is true for two unit vector

\hat{A}

and

\hat{B}

making an angle

θ

to each other?

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}

, the angle between

\vec{P}

and

\vec{Q}

θ (0 ° < θ < 360 °)

. The value of

θ

will be ___

°

MEDIUM

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

The sum of two forces

\vec{P}

and

\vec{Q}

\vec{R}

such that

|\vec{R}| = |\vec{P}|

. The angle

θ

(in degree) that the resultant of

2 \vec{P}

and

\vec{Q}

will make with

\vec{Q}

is, ________

EASY

Physics>General Physics>Mathematical Tools in Physics>Multiplication of Vectors

Let

\vec{A} = (\hat{i} + \hat{j}) a n d \vec{B} = (2 \hat{i} - \hat{j})

. The magnitude of a coplanar vector

\vec{C}

such that

\vec{A} . \vec{C} = \vec{B} . \vec{C} = \vec{A} . \vec{B}

is given by:

If two vectors 2i^+3j^-k^ and -4i^-6j^-λk^ are parallel, then find the value of λ.

Important Questions on Mathematical Tools in Physics

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If two vectors $2 \hat{i} + 3 \hat{j} - \hat{k}$ and $- 4 \hat{i} - 6 \hat{j} - λ \hat{k}$ are parallel, then find the value of $λ$ .