EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Afternoon>Q 31

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Let $\vec{u}$ and $\vec{v}$ be two non-zero vectors with the intermediate angle $45 °$ . Then $| \vec{u} \times \vec{v} | =$

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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 - 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

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2019 (21-Apr Shift-2)>Q 33

If

\vec{V} = 2 \hat{i} + \hat{j} - \hat{k}, \vec{W} = \hat{i} + 3 \hat{k}

and

\vec{U}

is a unit vector, then the maximum value of

[\begin{matrix} \vec{U} & \vec{V} & \vec{W} \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 34

If the volume of the parallelopiped formed by the vectors

\hat{i} + a \hat{j} + \hat{k}, \hat{j} + a \hat{k}

and

a \hat{i} + \hat{k}

becomes minimum, then

a =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Afternoon)>Q 35

Let

\vec{a}, \vec{b}, \vec{c}

be three-unit vectors and

\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0

. If the angle between

\vec{b}

and

\vec{c}

is

\frac{π}{3}

, then

[\vec{a} \vec{b} \vec{c}]^{2} =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Afternoon>Q 36

Let

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

and

\vec{c} = \hat{k} - \hat{i}

. If

\vec{d}

is a unit vector such

\vec{a} \cdot \vec{d} = 0 = [\begin{matrix} \vec{b} & \vec{c} & \vec{d} \end{matrix}],

then

\vec{d}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 37

If

\vec{a}, \vec{b} & \vec{c}

are non-coplanar vectors, then the point of intersection of the line passing through the points

2 \vec{a} + 3 \vec{b} - \vec{c}, 3 \vec{a} + 4 \vec{b} - 2 \vec{c}

with the line joining the points

\vec{a} - 2 \vec{b} + 3 \vec{c}

,

\vec{a} - 6 \vec{b} + 6 \vec{c}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET - 20 Aug 2021 Afternoon>Q 38

The equation of the plane passing through

3 \hat{i} + 2 \hat{j} + 6 \hat{k}

and parallel to the vectors

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

and

i - j + k

is