EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Forenoon)>Q 20

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Angle made by the position vector of the point $(5, - 4, - 3)$ with the positive direction of $X -$ axis is

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Important Questions on Vector Algebra

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Forenoon)>Q 21

If

\vec{a} = \frac{3}{2} \hat{k}, \vec{b} = \frac{2 \hat{i} + 2 \hat{j} - \hat{k}}{2}

, then angle between

\vec{a} + \vec{b}

and

\vec{a} - \vec{b}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Forenoon)>Q 23

If

\vec{a} = 2 \hat{i} + \hat{j} + 3 \hat{k}, \vec{b} = \hat{i} + 3 \hat{j} - \hat{k}

and

\vec{c} = 3 \hat{i} - \hat{j} - 2 \hat{k}

then, the value of

|\begin{matrix} \vec{a} \cdot \vec{a} & \vec{a} \cdot \vec{b} & \vec{a} \cdot \vec{c} \\ \vec{b} \cdot \vec{a} & \vec{b} \cdot \vec{b} & \vec{b} \cdot \vec{c} \\ \vec{c} \cdot \vec{a} & \vec{c} \cdot \vec{b} & \vec{c} \cdot \vec{c} \end{matrix}|

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Forenoon)>Q 24

If

\vec{a}

and

\vec{b}

are two vectors such that

| \vec{a} | = 2, | \vec{b} | = 3

and

\vec{a} + t \vec{b}

and

\vec{a} - t \vec{b}

are perpendicular, where

' t'

is a positive scalar, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Afternoon)>Q 27

If the projections of the line segment

\vec{A B}

on

X Y, Y Z

and

Z X

planes are

\sqrt{15}, \sqrt{46}, 7

respectively, then the projection of

\vec{A B}

on

y -

axis is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Forenoon>Q 28

Let

\vec{u} = 2 \hat{i} + 3 \hat{j} + \hat{k}, \vec{v} = - 3 \hat{i} + 2 \hat{j}

and

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

, Then which of the following statement is true?

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Forenoon>Q 29

If

\vec{a} = (1, 1, 0), \vec{b} = (1, 1, 1)

, then unit vector in the plane of

\vec{a}

and

\vec{b}

and perpendicular to

\vec{a}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Afternoon>Q 30

The value of

\frac{(\vec{a} \times \vec{b})^{2} + (\vec{a} \cdot \vec{b})^{2}}{2 (\vec{a})^{2} (\vec{b})^{2}}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Afternoon>Q 32

Given

\vec{a} = 3 \hat{i} - \hat{j}, \vec{b} = 2 \hat{i} + \hat{j} - 3 \hat{k}

and

\vec{b} = \vec{b_{1}} + \vec{b_{2}}

, where

\vec{b_{1}}

is parallel to

\vec{a}

and

\vec{b_{2}}

is perpendicular to

\vec{a}

then

\vec{b_{2}}

is equal to