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

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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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Important Questions on Vector Algebra

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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} | =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET - 5 August 2021 Shift 2>Q 28

If

\vec{b} = 2 \hat{i} - \hat{j} - \hat{k}, \vec{a} = 3 \hat{i} + 4 \hat{j} - 5 \hat{k}

and

\vec{b} \times (\vec{a} \times \vec{b}) = \frac{\vec{a} - k \vec{b}}{l}

then

\frac{k}{l | \vec{b} |}

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 29

If

\vec{r}

is a unit vector satisfying

\vec{r} \times \vec{a} = \vec{b}, | \vec{a} | = 2

and

| \vec{b} | = \sqrt{3},

then one such

\vec{r} =

HARD

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2020 (9-Sep Shift-1)>Q 30

A (\vec{a}), B (\vec{b}), C (\vec{c}), D (\vec{d})

are four concyclic points, such that

x \vec{a} + y \vec{b} + z \vec{c} + t \vec{d} = \vec{0}, x + y + z + t = 0

, where

x, y, z, t

are constants not all zero. If the chords

A B

and

C D

intersect at

P

, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2020 (9-Sep Shift-1)>Q 31

If

A (1, 2, 3), B (3, 7, - 2), C (6, 7, 7)

and

D (- 1, 0, - 1)

are points in a plane, then the vector equation of the line passing through the centroids of

Δ A B D

and

Δ A C D

is