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 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 32

If

\vec{u} = \vec{a} - \vec{b}, \vec{v} = \vec{a} + \vec{b}, | \vec{a} | = | \vec{b} | = 2

then

| \vec{u} \times \vec{v} |

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 37

A unit vector perpendicular to the plane passing through the points whose position vectors are

\hat{i} - \hat{j} + 2 \hat{k}, 2 \hat{i} - \hat{k}

and

2 \hat{i} + \hat{k}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 38

Let

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

be the position vectors of three vertices

A, B, C

of a triangle respectively. Then the area of the triangle is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 41

The vectors

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}

and

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

are coplanar if the value of

λ

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 48

If

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

are three non-coplanar vectors such that

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

and

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

then

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

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 52

Let

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

and

\vec{b}

be another vector such that

\vec{a} \cdot \vec{b} = 14

and

\vec{a} \times \vec{b} = 3 \hat{i} + \hat{j} - 8 \hat{k},

then

\vec{b} = b_{1} \hat{i} + \hat{j} + b_{2} \hat{k}

then

(b_{1}^{b_{2}})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment>Q 5

A vector

\vec{c}

of magnitude

\sqrt{7}

which is perpendicular to the vector

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

and

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

and makes an obtuse angle with the

y

-axis is given by