Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 11

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If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of $x$ for which vectors $\vec{α} = (x - 2) \vec{a} + \vec{b}$ and $\vec{β} = (3 + 2 x) \vec{a} - 2 \vec{b}$ are collinear, is given by

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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 12

Let

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

are three non-zero vectors such that any two of them are non-collinear. If

\vec{a} + \vec{b}

is collinear with

\vec{c}

and

\vec{b} + \vec{c}

is collinear with

\vec{a},

then the value of

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

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.2>Q 13

If

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

and

\vec{c} = \hat{i} + α \hat{j} + β \hat{k}

are linearly dependent vectors and

| \vec{c} | = \sqrt{3},

then

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

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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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