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

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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

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Important Questions on Vector Algebra

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IMPORTANT

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

The vector that is parallel to the vector

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

and coplanar with the vectors

\hat{i} + \hat{j}

and

\hat{j} + \hat{k}

is

EASY

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-2)>Q 2

Consider the vectors $\vec{a} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k}, \vec{b} = 6 \hat{i} - 2 \hat{j} + 3 \hat{k}$ and $\vec{c} = 3 \hat{i} - 6 \hat{j} - 2 \hat{k}$

Assertion (A): The three vectors do not form a triangle

Reason (R): The three vectors are non-coplanar

The correct option among the following is

MEDIUM

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-2)>Q 3

Let

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

If

\vec{b} = \vec{c} - \vec{d}, \vec{a}

is parallel to

\vec{c}

and perpendicular to

\vec{d}

, then

\vec{c} + \vec{d} =

MEDIUM

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-2)>Q 4

Let

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

be four vectors such that

\vec{a}

is perpendicular only to

\vec{c}

. The vector

\vec{b}

is parallel to

(\vec{c} - \vec{d})

then

\vec{c} =

MEDIUM

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2020 (9-Sep Shift-1)>Q 5

If

\vec{a}

and

\vec{b}

are two non-collinear vectors, then

\frac{\vec{a} \times (\vec{b} \times \vec{a})}{{|\vec{a}|}^{2}}

represent

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2020 (9-Sep Shift-1)>Q 6

If

\vec{a} = \hat{i} + (\tan θ) \hat{j} + (\frac{3}{\sqrt{\sin \frac{θ}{2}}}) \hat{k}

and

\vec{b} = \tan θ (\hat{j} - \hat{i}) - (2 \sqrt{\sin \frac{θ}{2}}) \hat{k}

are orthogonal vectors and

\vec{c} = (\sin 2 θ) \hat{i} - 2 \hat{j} + 2 \hat{k}

makes an obtuse angle with

X

-axis, then

θ =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2020 (9-Sep Shift-1)>Q 7

If

\vec{a} + l \vec{b} + l^{2} \vec{c} = 0

and

\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = 3 (\vec{b} \times \vec{c}),

then the minimum value of such

l

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 8

If

\bar{O A} = \bar{i} + 2 \bar{j} + 3 \bar{k}

and

\bar{O B} = 4 \bar{i} + \bar{k}

are the position vectors of the points

A

and

B

, then the position vector of a point on the line passing through

B

and parallel to the vector

\bar{O A} \times \bar{O B}

which is at a distance of

\sqrt{189}

units from

B

is