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

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IMPORTANT

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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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Important Questions on Vector Algebra

HARD

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IMPORTANT

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 =

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 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

EASY

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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

EASY

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2019 (03-May Shift-2)>Q 9

A vector

\vec{a}

of length

2

units is making an angle

60 °

with each of the

X

-axis and

Y

-axis. If another vector

\vec{b}

of length

\sqrt{2}

units is making an angle

45 °

with each of the

Y

-axis and

Z

-axis, then

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

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2019 (03-May Shift-2)>Q 10

The length of the projection of the line segment joining the points

(3, 4, 5)

and

(4, 6, 3)

on the line joining the points

(- 1, 2, 4)

and

(1, 0, 5)

is

EASY

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-1)>Q 11

If the vectors

- 3 \hat{i} + 4 \hat{j} + λ \hat{k}

and

μ \hat{i} + 8 \hat{j} + 6 \hat{k}

are collinear, then

λ - μ =

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-1)>Q 12

The angle between the vectors

2 \hat{k} - 3 \hat{j}

and

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

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>TS EAMCET 2021 (04-Aug Shift-1)>Q 13

Three vectors

\vec{a}, \vec{b}

and

\vec{c}

satisfy

\vec{a} + \vec{b} + \vec{c} = \vec{0} .

If

|\vec{a}| = 3, |\vec{b}| = 4, |\vec{c}| = 2,

then

\vec{a} . \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} . \vec{a} + 2 (| \vec{a} | + | \vec{b} | + | \vec{c} |) =