Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 28

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The vectors $\hat{i} - 2 x \hat{j} - 3 y \hat{k}$ and $\hat{i} + 3 x \hat{j} + 2 y \hat{k}$ are orthogonal to each other. Then, the locus of the point $(x, y)$ is

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Important Questions on Vector Algebra

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 29

For what value of

λ

, the vectors

λ \hat{i} + (1 + λ) \hat{j} + (1 + 2 λ) \hat{k}

and

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

are perpendicular to each other.

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 30

If

|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|

, then which one of the following is correct?

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 31

If

\vec{a}

and

\vec{b}

are vectors such that

| \vec{a} | = 2,

| \vec{b} | = 7

and

\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6 \hat{k},

then what is the acute angle between

a

and

b

?

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 32

If

\vec{u} = \vec{a} - \vec{b}, \vec{v} = \vec{a} + \vec{b}

and

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

, then

|\vec{u} \times \vec{v}|

is equal to

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 33

If

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

and

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

, then what is the value of

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

?

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 34

If

(3 \vec{a} - \vec{b}) \times (\vec{a} + 3 \vec{b}) = k \vec{a} \times \vec{b}

, then what is the value of

k

?

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 35

The area of parallelogram whose adjacent sides are

\vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + \hat{k}

is

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Mathematics Crash Course NDA & NA EE>Chapter 29 - Vector Algebra>Exercise 1>Q 36

If

\vec{a}

be any vector, then

{|\vec{a} \times \hat{i}|}^{2} + {|\vec{a} \times \hat{j}|}^{2} + {|\vec{a} \times \hat{k}|}^{2}

is equal to