Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 1

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If two pairs of opposite edges of a tetrahedron are perpendicular then-

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Important Questions on Vector Algebra

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 2

A non-zero vector

\vec{a}

is parallel to the line of intersection of the plane determined by the vectors

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

and the plane determined by the vectors

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

. The possible angle between

\vec{a}

and

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

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 3

Let

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

and

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

be three vectors. A vector in the plane of

\vec{b}

and

\vec{c}

whose projection on

\vec{a}

is of magnitude

\sqrt{\frac{2}{3}}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 4

Let

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

are three non-coplanar vectors such that

{\vec{r}}_{1} = \vec{a} - \vec{b} + \vec{c}

,

{\vec{r}}_{2} = \vec{b} + \vec{c} - \vec{a}

,

{\vec{r}}_{3} = \vec{c} + \vec{a} + \vec{b}

,

\vec{r} = 2 \vec{a} - 3 \vec{b} + 4 \vec{c} .

If

\vec{r} = ƛ_{1} {\vec{r}}_{1} + ƛ_{2} {\vec{r}}_{2} + ƛ_{3} {\vec{r}}_{3},

then

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 5

A point

M

is taken on side

\vec{A C}

of a triangle

A B C

, such that

\vec{A M} = \frac{1}{3} \vec{A C}

. A point

N

is taken on the side

\vec{C B}

such that

\vec{B N} = \vec{C B}

then, for the point of intersection

X

of

\vec{A B} & \vec{M N}

which of the following holds good?

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 6

Vector

\vec{A}

has components

A_{1}, A_{2}, A_{3}

along the three axes. If the co-ordinates system is rotated by

90 °

about

z

-axis, then the new components along the axis are

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 7

Let

\vec{p}, \vec{q}, \vec{r}

be three mutually perpendicular vectors of the same magnitude. If a vector

\vec{x}

satisfies the equation

\vec{p} \times ((\vec{x} - \vec{q}) \times \vec{p}) + \vec{q} \times ((\vec{x} - \vec{r}) \times \vec{q}) + \vec{r} \times ((\vec{x} - \vec{p}) \times \vec{r}) = \vec{0}

. Then

\vec{x}

is given by

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 8

A vector which makes equal angles with the vectors

\frac{1}{3} (\hat{i} - 2 \hat{j} + 2 \hat{k}), \frac{1}{5} (- 4 \hat{i} - 3 \hat{k})

and

\hat{j},

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 9

The triple product

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

simplifies to