EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET - 5 August 2021 Shift 1>Q 19

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If $\vec{a} = 2 \hat{i} + 2 \hat{j} + \hat{k}, \vec{|b|} = 6$ and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{π}{6},$ then the area of the triangle (in square units) with $\bar{a}$ and $\bar{b}$ as two of its sides 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>TS EAMCET - 5 August 2021 Shift 1>Q 20

The four points

A (2, - 1, 3), B (4, - 2, 1), C (4, 5, - 7)

and

D (2, 6, - 5)

forms a

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET - 5 August 2021 Shift 2>Q 21

Let

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

be unit vectors such that

2 \vec{a} + 3 \vec{b} + 4 \vec{c} = \vec{0} .

Then

| \vec{b} \times \vec{c} | =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2020 (9-Sep Shift-1)>Q 22

If

\vec{a}, \vec{b}

and

\vec{c}

be three non-coplanar vectors and

\vec{p}, \vec{q},

and

\vec{r}

be defined by

\vec{p} = \frac{\vec{b} \times \vec{c}}{\vec{a} \cdot (\vec{b} \times \vec{c})}, \vec{q} = \frac{\vec{c} \times \vec{a}}{\vec{b} \cdot (\vec{c} \times \vec{a})}, \vec{r} = \frac{\vec{a} \times \vec{b}}{\bar{c} \cdot (\vec{a} \times \vec{b})}

such that

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2018 (04-May Shift-1)>Q 23

The volume of a tetrahedron whose vertices are

4 \hat{i} + 5 \hat{j} + \hat{k}, - \hat{j} + \hat{k}, 3 \hat{i} + 9 \hat{j} + 4 \hat{k}

and

- 2 \hat{i} + 4 j + 4 \hat{k}

is (in cubic units)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2018 (04-May Shift-1)>Q 24

If the vectors

\vec{b}, \vec{c}, \vec{d}

are not coplanar, then, the vector

(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) + (\vec{a} \times \vec{c}) \times (\vec{d} \times \vec{b}) + (\vec{a} \times \vec{d}) \times (\vec{b} \times \vec{c})

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2019 (03-May Shift-2)>Q 25

Let

\vec{a}

be a non-zero vector. If

\vec{x} = \hat{i} \times (\vec{a} \times \hat{i}), \vec{y} = \hat{j} \times (\vec{a} \times \hat{j}) - \vec{a}

and

\vec{z} = \hat{k} \times (\vec{a} \times \hat{k}) - \vec{a},

then

[\begin{array}{l} \vec{x} & \vec{y} & \vec{z} \end{array}] =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-1)>Q 26

(\vec{a} + 2 \vec{b} - \vec{c}) . \{(\vec{a} - \vec{b}) \times (\vec{a} - \vec{b} - \vec{c})\} =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET - 5 August 2021 Shift 1>Q 27

If

\vec{r}

is a vector perpendicular to both the vectors

2 \hat{i} + 3 \hat{j} - 4 \hat{k}

and

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

and satisfy

\vec{r} . (3 \hat{i} - 3 \hat{j} + 4 \hat{k}) = 5

, then

| \vec{r} | =