Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 4

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The vector $\vec{P} = a \hat{i} + a \hat{j} + 3 \hat{k}$ and $\vec{Q} = a \hat{i} - 2 \hat{j} - \hat{k}$ are perpendicular to each other. The positive value of $a$ is,

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Important Questions on Mathematical Tools in Physics

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 5

A force

\vec{F} = (3 \hat{i} + 4 \hat{j}) N

acts on a body and displaces it by

\vec{S} = (3 \hat{i} + 4 \hat{j}) m

. The work done

(W = \vec{F} . \vec{S})

by the force is:

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 6

What is the projection of

(3 \hat{i} + 4 \hat{k})

on the

Y

-axis?

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 7

If a vector

2 \hat{i} + 3 \hat{j} + 8 \hat{k}

is perpendicular to the vector

4 \hat{j} - 4 \hat{i} + α \hat{k}

, then the value of

α

is

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 8

If

\vec{A} = 3 \hat{i} + 4 \hat{j}

and

\vec{B} = 6 \hat{i} + 8 \hat{j}

and

A

and

B

are the magnitudes of

\vec{A}

and

\vec{B}

, then which of the following is not true?

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 9

A vector

\vec{F_{1}}

is along the positive

X

-axis. If its vector product with another vector

\vec{F_{2}}

is zero then

\vec{F_{2}}

maybe:

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 10

If

\hat{i}, \hat{j}

and

\hat{k}

are unit vectors along

X, Y

and

Z

axis respectively, then tick the wrong statement:

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 11

Two vectors

\vec{P}

and

\vec{Q}

are inclined to each other at angle

θ

. Which of the following is the unit vector, perpendicular to

\vec{P}

and

\vec{Q}

?

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Analytical Questions)>Q 12

The magnitude of the vector product of two vectors

\vec{A}

and

\vec{B}

may not be :