Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 50

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If $\vec{a} = (\hat{i} + \hat{j} + \hat{k}),$ $\vec{a} \cdot \vec{b} = 1$ and $\vec{a} \times \vec{b} = \hat{j} - \hat{k}$ , then $\vec{b}$ is

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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 51

Let

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

be three vectors such that

| \vec{a} | = | \vec{b} | = | \vec{c} | = 6

and angle between

\vec{a}

and

\vec{b}, \vec{b}

and

\vec{c}

and

\vec{c}

and

\vec{a}

is

\frac{π}{3}

each then the volume of the triangular prism whose adjacent edges are represented by vectors

\vec{a}, \vec{b}

and

\vec{c}

is

\sqrt{2} v

then

v

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 Set-2>Q 53

P

be any point on the circumcircle of the equilateral triangle of side length

6

units, then the value of

| \vec{P A} |^{2} + | \vec{P B} |^{2} + | \vec{P C} |^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment Set-2>Q 54

Let

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

are three vectors such that

[\vec{a} \vec{b} \vec{c}] = 10

then the value of

[2 \vec{a} - \vec{b} 3 \vec{b} - \vec{c} 2 \vec{c} - \vec{a}]

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment>Q 1

Let

\vec{a} = 3 \hat{i} - \hat{j}, \vec{b} = \hat{i} - 2 \hat{j}, \vec{c} = - \hat{i} + 7 \hat{j}

and

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

Then

\vec{P}

in terms of

\vec{a}

and

\vec{b}

is

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

If

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

and

\vec{d}

are the position vectors of points

A, B, C, D

such that no three of them are collinear and

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

, then

A B C D

is a

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment>Q 3

If

\vec{O A} = \vec{a}; \vec{O B} = \vec{b}; \vec{O C} = 2 \vec{a} + 3 \vec{b}, \vec{O D} = \vec{a} - 2 \vec{b},

the length of

\vec{O A}

is three times the length of

\vec{O B}

and

\vec{O A}

is perpendicular to

\vec{D B},

then

(\vec{B D} \times \vec{A C}) \cdot (\vec{O D} \times \vec{O C})

is

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>Assignment>Q 4

Let

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

be three unit vectors, such that

|\vec{a} + \vec{b} + \vec{c}| = 1

and

\vec{a}

is perpendicular to

\vec{b}

If

\vec{c}

makes angles

α

and

β

with

\vec{a}

and

\vec{b}

respectively, then

\cos α + \cos β =