EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 18

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If $\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k}, \vec{b} = \hat{i} - 2 \hat{j} + \hat{k}, \vec{c} = - \hat{i} + \hat{j} - 4 \hat{k}$ and $\bar{d} = \hat{i} + \hat{j} + \hat{k},$ then $| (\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) | =$

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Important Questions on Vector Algebra

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AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 19

If the vertices of

Δ ABC

are

A = (2, 3, 5), B = (- 1, 3, 2), C = (3, 5, - 2),

then the area of the

Δ ABC

(in sq. units) is

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

Angle made by the position vector of the point

(5, - 4, - 3)

with the positive direction of

X -

axis is

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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

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Forenoon)>Q 22

If

\vec{a} = \hat{\dot{i}} + \hat{\dot{j}} + \hat{k}, \vec{b} = \hat{\dot{i}} + 3 \hat{\dot{j}} + 5 \hat{k}

and

\vec{c} = 7 \hat{\dot{i}} + 9 \hat{\dot{j}} + 11 \hat{k}

then the area of parallelogram having diagonals

\vec{a} + \vec{b}

and

\vec{b} + \vec{c}

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 25

If

\vec{a}

and

\vec{b}

are two vectors such that

\frac{\vec{a} \cdot \vec{b}}{| \vec{a} | | \vec{b} |} < 0

and

| \vec{a} \cdot \vec{b} | = | \vec{a} \times \vec{b} |

, then the angle between the vectors

\vec{a}

and

\vec{b}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2021 (19-Aug Afternoon)>Q 26

Let

x, y

are real numbers. If

\vec{a} = (\sin x) \hat{i} + (\sin y) \hat{j}

and

\vec{b} = (\cos x) \hat{i} + (\cos y) \hat{j}

, then

| \vec{a} \times \vec{b} |

is