Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 45

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If $\vec{a} \times \vec{b} = \vec{c},$ $\vec{b} \times \vec{c} = \vec{a},$ then find value of $|3 \vec{a} + 4 \vec{b} + 12 \vec{c}|$ if $\vec{a},$ $\vec{b},$ $\vec{c}$ are vectors of same magnitude.

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Important Questions on Vector Algebra

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 46

Angle between diagonals of a parallelogram whose side are represented by

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

and

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

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 47

A,

B,

C

&

D

are four points in a plane with position vectors

\vec{a},

\vec{b},

\vec{c}

&

\vec{d}

, respectively such that

(\vec{a} - \vec{d}) \cdot (\vec{b} - \vec{c}) = (\vec{b} - \vec{d}) \cdot (\vec{c} - \vec{a}) = 0 .

Then for the triangle

A B C,

D

is its

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 48

Given

| \vec{a} | = 10, | \vec{b} | = 2

and

\vec{a} \cdot \vec{b} = 12

, then find

| \vec{a} \times \vec{b} |

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 49

Unit vector perpendicular to the plane of the triangle

A B C

with position vectors

\vec{a},

\vec{b},

\vec{c}

of the vertices

A,

B,

C

is (where

∆

is the area of the triangle

A B C

).

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 50

Let

\vec{a} = \hat{i} + \hat{j}

and

\vec{b} = 2 \hat{i} - \hat{k} .

The point of intersection of the lines

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

and

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

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 51

The value of

[(\vec{a} + 2 \vec{b} - \vec{c}) (\vec{a} - \vec{b}) (\vec{a} - \vec{b} - \vec{c})]

is equal to the box product

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 52

For a non-zero vector

\vec{A}

if the equations

\vec{A} \cdot \vec{B} = \vec{A} \cdot \vec{C}

and

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

hold simultaneously, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-1>Q 53

Let

\vec{a} = x \hat{i} + 12 \hat{j} - \hat{k}, \vec{b} = 2 \hat{i} + 2 x \hat{j} + \hat{k}

and

\vec{c} = \hat{i} + \hat{k}

. If the ordered set

[\vec{b} \vec{c} \vec{a}]

is left-handed, then