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

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The area of parallelogram whose diagonals coincide with the following pair of vectors is $5 \sqrt{3} .$ The vectors are

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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 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

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 23

If

\vec{a}

is any vector, then

(\vec{a} \times \hat{i})^{2} + (\vec{a} \times \hat{j})^{2} + (\vec{a} \times \hat{k})^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 24

If

| \vec{a} \times \vec{b} | = 2, | \vec{a} \cdot \vec{b} | = 2,

then

| \vec{a} |^{2} | \vec{b} |^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 25

If

\vec{a}

and

\vec{b}

are unit vectors, then which of the following values of

\vec{a} . \vec{b}

is not possible?

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 26

If

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

and

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

then the angle between

\vec{a}

and

\vec{b}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 27

If

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

then

(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b})

is equal to