EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Vector Algebra>KEAM 2018>Q 20

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If $\vec{a}$ and $\vec{b} = 3 \hat{i} + 6 \hat{j} + 6 \hat{k}$ are collinear and $\vec{a} . \vec{b} = 27,$ then $\vec{a}$ is equal to

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Important Questions on Vector Algebra

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Vector Algebra>KEAM 2018>Q 21

Let

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

and

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

.

Then, the area of the parallelogram with diagonals

\vec{a} + \vec{b}

and

\vec{b} + \vec{c}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Vector Algebra>KEAM 2018>Q 22

If

|\vec{a}| = 13, |\vec{b}| = 5

and

\vec{a} \cdot \vec{b} = 30

,

then

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

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Vector Algebra>KEAM 2019>Q 23

The value of

[a - b, b - c, c - a]

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Vector Algebra>KEAM 2018>Q 24

If the vectors

4 \hat{i} + 11 \hat{j} + m \hat{k}, 7 \hat{i} + 2 \hat{j} + 6 \hat{k}

and

\hat{i} + 5 \hat{j} + 4 \hat{k}

are coplanar, then

m

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Vector Algebra>KEAM 2019>Q 25

If $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}, \vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 3 \hat{j} - 2 \hat{k}$ and $\vec{c} = - 2 \hat{i} + \hat{j} - 3 \hat{k}$ such that $\vec{r} = λ \vec{a} + μ \vec{b} + γ \vec{c}$ , then