Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 22

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If $\vec{a}, \vec{b} & \vec{c}$ are non-coplanar unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b} + \vec{c}}{\sqrt{2}}$ , then the angle between

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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 23

If

\vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e}, \vec{f}

are position vectors of

6

points

A, B, C, D, E

and

F

respectively such that

3 \vec{a} + 4 \vec{b} = 6 \vec{c} + \vec{d} = 4 \vec{e} + 3 \vec{f} = \vec{x}

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 24

The vector

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

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 25

If a vector

\vec{r}

of magnitude

3 \sqrt{6}

is collinear with the bisector of the angle between the vector

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

and

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

, then

\vec{r} =

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

Faces

A B C

and

B C D

of a tetrahedron

A B C D

meet at an angle of

30 °

. The area of face

A B C

is

120

sq. units and the area of face

B C D

is

80

sq. units and

B C = 10

units, then the volume of tetrahedron is

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

In

∆ A B C

, Let

B (3, 3, - 9)

and

A B = A C

and altitude

A D

is

\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z + 3}{3}

. If coordinates of

C

are

(α, β, γ)

, then

|α| + |β| + |γ|

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-3>Q 13

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

and

\vec{d}

are the position vectors of the points

A \equiv (x, y, z); B \equiv (y, - 2 z, 3 x); C \equiv (2 z, 3 x, - y)

and

D \equiv (1, - 1, 2)

respectively. If

|\vec{a}| = 2 \sqrt{3}; (\vec{a}^\vec{b}) = (\vec{a}^\vec{c}); (\vec{a}^\vec{d}) = \frac{π}{2}

and

(\vec{a}^\vec{j})

is obtuse, then the value of

(x + y + z)

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-3>Q 14

Let

\vec{u}

be a vector on rectangular coordinate system with sloping angle

60 °

. Suppose that,

|\vec{u} - \hat{i}|

is geometric mean of

|\vec{u}|

and

|\vec{u} - 2 \hat{i}|

where

\hat{i}

is the unit vector along

x

-axis then

|\vec{u}|

has the value equal to

\sqrt{a} - \sqrt{b}

where

a, b \in N .

Then the value of

{(a + b)}^{3} + {(a - b)}^{3}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-3>Q 15

Let

\vec{A} = 2 \vec{i} + \vec{k}, \vec{B} = \vec{i} + \vec{j} + \vec{k}

and

\vec{C} = 4 \vec{i} - 3 \vec{j} + 7 \vec{k}

, then the vector

\vec{R}

, satisfying

\vec{R} \times \vec{B} = \vec{C} \times \vec{B}

and

\vec{R} \cdot \vec{A} = 0,

is

x \hat{i} + y \hat{j} + z \hat{k}

, then

(x + y + z)

is equal to