Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 31

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The vertices of a triangle are $A (1, 1, 2), B (4, 3, 1)$ and $C (2, 3, 5) .$ A vector representing the bisector of the angle $A$ is:

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Important Questions on Vector Algebra

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 32

The vector

\vec{c},

parallel to the internal bisector of the angle between the vectors

\vec{a} = 7 \hat{i} - 4 \hat{j} - 4 \hat{k}

and

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

with

|\vec{c}| = 5 \sqrt{6},

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 34

\hat{a}

and

\hat{b}

are two given unit vectors at right angle. The unit vector equally inclined with

\hat{a}, \hat{b}

and

\hat{a} \times \hat{b}

will be

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 36

The position vectors of the angular points of a tetrahedron are

A (3 \hat{i} - 2 \hat{j} + \hat{k}), B (3 \hat{i} + \hat{j} + 5 \hat{k}), C (4 \hat{i} + 3 \hat{k})

and

D (\hat{i})

. Then the acute angle between the lateral face

A D C

and the base face

A B C

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 37

If

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

and

\vec{d}

are unit vectors such that

(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) = λ

and

\vec{a} \cdot \vec{c} = \frac{\sqrt{3}}{2},

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 38

The coplanar points

A, B, C, D

are

(2 - x, 2, 2), (2, 2 - y, 2), (2, 2, 2 - z)

and

(1, 1, 1)

, respectively, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 39

Which of the following statement

(s)

is/are correct?

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 40

Let

\vec{V} = 2 \hat{i} + \hat{j} - \hat{k} & \vec{W} = \hat{i} + 3 \hat{k .}

If

\vec{U}

is a unit vector, then the value of the scalar triple product

[\vec{U} \vec{v} \vec{w}]

may be

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 41

If

\vec{A} + \vec{B} = \vec{a}, \vec{A} \cdot \vec{a} = 1

and

\vec{A} \times \vec{B} = \vec{b}

, then