Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 14

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If $\hat{x}, \hat{y}, \hat{z}$ are mutually perpendicular unit vectors and $a \hat{x} + a \hat{y} + c \hat{z}, \hat{x} + \hat{z}$ and $c \hat{x} + c \hat{y} + b \hat{z}$ are coplanar, then

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Important Questions on Vector Algebra

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 15

If

|\vec{a}| = 1, |\vec{b}| = 2, |\vec{c}| = 3

and

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

then the value of

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

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 16

ABCD is parallelogram with

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

and

\vec{B D} = - \hat{i} + 2 \hat{j} - 5 \hat{k} .

Then area of this parallelogram is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 17

The unit vector perpendicular to the plane of vectors

\hat{i} + \hat{j} + \hat{k}

and

\hat{i} + \hat{j},

is given by

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 18

If

' θ'

is the angle between the unit vectors

\vec{a}

and

\vec{b},

then

\sin \frac{θ}{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 19

If

|\begin{array}{l} a & a^{2} & 1 + a^{3} \\ b & b^{2} & 1 + b^{3} \\ c & c^{2} & 1 + c^{3} \end{array}| = 0

and the vectors

A \equiv (1, a, a^{2})

B \equiv (1, b, b^{2}), C \equiv (1, c, c^{2})

are non-coplanar, then the value of

(a b c)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 20

If the vectors

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

are coplanar, then the value of

|\begin{matrix} \vec{a} & \vec{b} & \vec{c} \\ \vec{a} \cdot \vec{a} & \vec{a} \cdot \vec{b} & \vec{a} \cdot \vec{c} \\ \vec{b} \cdot \vec{a} & \vec{b} \cdot \vec{b} & \vec{b} \cdot \vec{c} \end{matrix}| =

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 21

If

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

are three non-coplanar, non-zero vectors, then value of

(\vec{a} \cdot \vec{a}) (\vec{b} \times \vec{c}) + (\vec{a} \cdot \vec{b}) (\vec{c} \times \vec{a}) + (\vec{a} \cdot \vec{c}) (\vec{a} \times \vec{b})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 22

The vectors

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

and

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

are