Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 13

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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 14

Given a parallelogram

O A C B

. The length of the vectors

\vec{O A}, \vec{O B} & \vec{A B}

are

a, b & c

respectively. The scalar product of the vectors

\vec{O C} & \vec{O B}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 15

Consider

△ A B C

with

A = \vec{(a)}, B = (\vec{b}) and C = (\vec{c})

. If

\vec{b} \cdot (\vec{a} + \vec{c}) = \vec{b} \cdot \vec{b} + \vec{a} \cdot \vec{c}, |\vec{b} - \vec{a}| = 3 and |\vec{c} - \vec{b}| = 4

, then the angle between the medians

A M, B D

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 16

If the non zero vectors

\vec{a}

&

\vec{b}

are perpendicular to each other then the solution of the equation

\vec{r} \times \vec{a} = \vec{b}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 17

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

be three coplanar vectors and

\vec{r}

be any arbitrary vector, then

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

is equal to-

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 18

\vec{a}

and

\vec{b}

are mutually perpendicular unit vectors.

\vec{r}

is a vector satisfying

\vec{r} \cdot \vec{a} = 0, \vec{r} \cdot \vec{b} = 1

and

[\begin{matrix} \vec{r} & \vec{a} & \vec{b} \end{matrix}] = 1,

then

\vec{r}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 19

A B C D

is a parallelogram.

E

and

F

be the middle points of the sides

A B

and

B C

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 21 - Vector Algebra>EXERCISE-2>Q 20

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

are mutually perpendicular vectors of equal magnitude then angle between

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

and

\vec{a}

is

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

If

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

, where

\vec{a}, \vec{b}

and

\vec{c}

are any three vectors such that

\vec{a} \cdot \vec{b} \neq 0, \vec{b} \cdot \vec{c} \neq 0

then

\vec{a}

and

\vec{c}

are