Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 14

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If $O A C B$ is a parallelogram with $\vec{O C} = \vec{a}$ and $\vec{A B} = \vec{b,}$ then $\vec{O A}$ is equal to

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Important Questions on Vector Algebra

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 15

Let

A B C D

be a parallelogram whose diagonals intersect at

P

and let

O

be the origin, then

\vec{O A} + \vec{O B} + \vec{O C} + \vec{O D}

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 16

\vec{a}

and

\vec{b}

are the position vectors of

A, B

respectively and

C

is a point on

A B

produced such that

A C = 3 A B .

Then the position vector of

C

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 17

If the points with position vectors

60 \hat{i} + 3 \hat{j}, 40 \hat{i} - 8 \hat{j}

and

a \hat{i} - 52 \hat{j}

are collinear, then

a

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 18

Given two vectors

\vec{a} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k}, \vec{b} = - 2 \hat{i} + 2 \hat{j} - \hat{k}

and

λ = \frac{the projection of \vec{a} on \vec{b}}{the projection of \vec{b} on \vec{a}}

, then the value of

λ

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 19

The area of parallelogram whose diagonals coincide with the following pair of vectors is

5 \sqrt{3} .

The vectors are

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 20

Let

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

be three nonzero vectors such that

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

and

λ \vec{b} \times \vec{a} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \vec{0},

then

λ

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 21

If

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

where

\vec{c} \neq 0

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 22

\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{i} \times \hat{j})

is equal to