Assertion ( A ) : If a → , b → are two non-collinear vectors then the vector component of b → along the line perpendicular to a → is a → × b → × a → a → 2 . Reason R : a → × b → × c → = a → · c → b → - a → · b → c → and vector component of b → on c → is b → · c → c → c → c → .

Both ( A ) and ( R ) are true and ( R ) is the correct explanation of ( A )

Both ( A ) and ( R ) are true but ( R ) is not the correct explanation of ( A )

( A ) is true but ( R ) is false

( A ) is false but ( R ) is true

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The area of the parallelogram, whose diagonals are $2 \hat{i} - \hat{j} + \hat{k}$ and $\hat{i} + 3 \hat{j} - \hat{k},$ is equal to

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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>AP EAPCET 2020 (Sep-23 Shift-1)>Q 10

The scalar product of the vector

\vec{a} = \hat{i} + \hat{j} + \hat{k}

with a unit vector along the sum of the vectors

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

and

\vec{c} = λ \hat{i} + 2 \hat{j} + 3 \hat{k}

is equal to one. Then.

λ =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2019 (21-Apr Shift-2)>Q 11

Let

D

and

E

be the midpoints of the sides

A C

and

B C

of a triangle

A B C

respectively. If

O

is an interior point of the triangle

A B C

such that

\vec{O A} + 2 \vec{O B} + 3 \vec{O C} = \vec{0},

then the area (in sq. units) of the triangle

O D E

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2019 (21-Apr Shift-2)>Q 12

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

are non-zero non-collinear vectors and

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

then

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

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2019 (21-Apr Shift-2)>Q 13

Assertion

(A) :

\vec{a}, \vec{b}

are two non-collinear vectors then the vector component of

\vec{b}

along the line perpendicular to

\vec{a}

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

.
Reason

(R) : \vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c}

and vector component of

\vec{b}

\vec{c}

(\vec{b} \cdot \frac{\vec{c}}{|\vec{c}|}) \frac{\vec{c}}{|\vec{c}|}

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 14

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

are three vectors such that

| \vec{a} | = 3, | \vec{b} | = 5, | \vec{c} | = 7

\bar{a}, \bar{b}, \bar{c}

are perpendicular to the vectors

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

respectively, then

\sqrt{{(\vec{a} + \vec{b} + \vec{c})}^{2} - 2} =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 15

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

are unit vectors and the maximum value of

| \vec{a} - \vec{b} |^{2} + | \vec{b} - \vec{c} |^{2} + | \vec{c} - \vec{a} |^{2}

k,

then

k (2 {\vec{a}}^{2} + 3 {\vec{b}}^{2} - 4 {\vec{c}}^{2}) =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 16

Let

\vec{a} = 2 \hat{i} + \hat{j} - 2 \hat{k}

and

\vec{b} = \hat{i} + \hat{j}

be two vectors.

\bar{c}

is a vector such that

\vec{a} \cdot \vec{c} = |\vec{c}|

and

|\vec{c} - \vec{a}| = 2 \sqrt{2}

. If the angle between

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

and

\vec{c}

30 °,

then

|(\vec{a} \times \vec{b}) \times \vec{c}|

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Vector Algebra>AP EAPCET 2018 (25-APR Shift-1)>Q 17

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

and

\vec{c} = \hat{i} - \hat{j}

and if

6 \hat{i} + 2 \hat{j} + 3 \hat{k} = λ_{1} (\vec{a} \times \vec{b}) + λ_{2} (\vec{b} \times \vec{c}) + λ_{3} (\vec{c} \times \vec{a}),

then

(λ_{1}, λ_{2}, λ_{3}) =

The area of the parallelogram, whose diagonals are 2i^-j^+k^ and i^+3j^-k^, is equal to

Important Questions on Vector Algebra

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The area of the parallelogram, whose diagonals are $2 \hat{i} - \hat{j} + \hat{k}$ and $\hat{i} + 3 \hat{j} - \hat{k},$ is equal to