Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 9

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$X -$ component of $\vec{a}$ is twice of its $Y$ -component. If the magnitude of the vector is $5 \sqrt{2}$ and it makes an angle of $135 °$ with $z$ -axis then the components of vector is :

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Important Questions on Mathematical Tools in Physics

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 10

If

\vec{a}

is a vector and

x

is a non-zero scalar, then

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 11

The two vectors

\vec{A}

and

\vec{B}

are drawn from a common point and

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

then angle between

\vec{A}

and

\vec{B}

is

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 12

Which of the following expressions are meaningful?

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 13

If the vectors

\vec{a}, \vec{b}

and

\vec{c}

from the sides

B C, C A

and

A B

respectively of a

Δ A B C

, then

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 14

Following forces start acting on a particle at rest at the origin of the coordinate system simultaneously.

\vec{F_{1}} = - 4 \hat{i} - 5 \hat{j} + 5 \hat{k}, \vec{F_{2}} = 5 \hat{i} + 8 \hat{j} + 6 \hat{k}, \vec{F_{3}} = - 3 \hat{i} + 4 \hat{j} - 7 \hat{k}

and

{\vec{F}}_{4} = 2 \hat{i} - 3 \hat{j} - 2 \hat{k}

, then the particle will move

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 15

The line of action of a force

\vec{F} = (- 3 \hat{i} + \hat{j} + 5 \hat{k}) N

passes through a point

(7, 3, 1)

. The moment of force

(\vec{τ} = \vec{r} \times \vec{F})

about the origin is given by

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 16

Position vector of a particle is given by

\vec{r} = acosωt \hat{i} + asinωt \hat{j}

. Which of the following is/are true?

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Beta Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 17

The magnitude of scalar product of two vectors is

8

and that of vector product is

8 \sqrt{3}

. The angle between them is