A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 42

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If $\vec{a}$ and $\vec{b}$ are two vectors then the value of $(\vec{a} + \vec{b}) \times (\vec{a} - \vec{b})$ is

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Important Questions on Scalars and Vectors

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 43

A body was at rest. Four forces begin to act on it simultaneously. The forces are

{\vec{F}}_{1} = \hat{i} + \hat{k}, {\vec{F}}_{2} = 3 \hat{j} - 4 \hat{i}, {\vec{F}}_{3} = 2 \hat{j} + 3 \hat{k}, {\vec{F}}_{4} = 3 \hat{i}

. In which plane will the body move ?

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 44

Two vectors

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

and

\vec{D} = \vec{A} - \vec{B}

are perpendicular to each other then

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 45

\vec{A}

and

\vec{B}

are two perpendicular vectors in a plane.

\vec{C}

is another vector perpendicular to the plane containing vectors

\vec{A}

and

\vec{B}

. Which of the following relations is/are possible?

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 46

Which of the following is incorrect?

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 47

Two particles having position vectors

\vec{r_{1}} = (3 \hat{i} + 5 \hat{j})

metre and

\vec{r_{2}} = (- 5 \hat{i} - 3 \hat{j})

metre and moving with velocities

{\vec{V}}_{1} = (4 \hat{i} + 3 \hat{j}) m / s

and

{\vec{V}}_{2} = (a \hat{i} + 7 \hat{j}) m / s

. If they collide after

2

seconds, the value of

{}^{'}a^{'}

is

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 48

A particle is moving with velocity

\vec{V} = k (y \hat{i} + x \hat{j})

, where is

k

constant. The general equation for its path is

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 49

Vector

\vec{A}

has magnitude

5

units, lies in the

x y

-plane and points in a direction

120 °

from the direction of increasing

x

. Vector

\vec{B}

has magnitude of

9

units and points along the

Z

-axis. The magnitude of cross product

\vec{A} \times \vec{B}

is

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 4 - Scalars and Vectors>EXERCISE>Q 50

If

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

and

\vec{A}, \vec{B}, \vec{C}

have scalar magnitudes of

5, 4, 3

units respectively, then the angle between

\vec{A}

and

\vec{C}

is