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Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. If magnitude of $\vec{A} + \vec{B}$ is equal to $n$ times the magnitude of $\vec{A} - \vec{B}$ then angle between $\vec{A}$ and $\vec{B}$ is,

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Important Questions on Scalars and Vectors

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 26

A unit vector is represented as

(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k})

. Hence, the value of

b

must be,

EASY

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 27

The angle between two vectors

A

and

B

θ

. Vector

R

is the resultant of the two vectors. If

R

makes an angle

\frac{θ}{2}

with

A

, then,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 28

The magnitude of the component of the vector

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

along

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

is,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 29

\vec{A}

and

\vec{B}

are two vectors given by,

\vec{A} = 2 \hat{i} + 3 \hat{j}

and

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

. The magnitude of the component of

\vec{A}

along

\vec{B}

is,

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 30

\vec{A} = 2 \hat{i} + 3 \hat{j} + 8 \hat{k}

is perpendicular to

\vec{B} = 4 \hat{j} - 4 \hat{i} + α \hat{k}

, then the value of

α

is,

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 31

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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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 32

Three vectors

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

and

\vec{C} = \hat{i} + \hat{j} + c \hat{k}

are mutually perpendicular.

\hat{i}, \hat{j}

and

\hat{k}

are unit vectors along

X, Y

and

Z

axis, respectively. The respective values of

a

b

and

c

are,

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IMPORTANT

MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 33

If vectors

\vec{A} = \cos (ω t) \hat{i} + \sin (ω t) \hat{j}

and

\vec{B} = \cos (\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,

Two vectors A→ and B→ have equal magnitudes. If magnitude of A→+B→ is equal to n times the magnitude of A→-B→ then angle between A→ and B→ is,

Important Questions on Scalars and Vectors

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Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. If magnitude of $\vec{A} + \vec{B}$ is equal to $n$ times the magnitude of $\vec{A} - \vec{B}$ then angle between $\vec{A}$ and $\vec{B}$ is,