Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 49

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IMPORTANT

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The vector $\vec{a} \times (\vec{b} \times \vec{a})$ is coplanar with

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Important Questions on Vector Algebra

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 50

If

\vec{a} \cdot \vec{b} = 0

and

\vec{a} \times \vec{b} = 0

, then which one of the following is correct?

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 51

The magnitude of the scalar

p

for which the vector

p (- 3 \hat{i} - 2 \hat{j} + 13 \hat{k})

is of unit length, is

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Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 52

What is the value of

λ

for which

(λ \hat{i} + \hat{j} - \hat{k}) \times (3 \hat{i} - 2 \hat{j} + 4 \hat{k}) = (2 \hat{i} - 11 \hat{j} - 7 \hat{k})

.

EASY

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Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 53

Consider the following statements:

$I$ . $4 \hat{i} \times 3 \hat{i} = 0$

$II$ . $\frac{4 \hat{i}}{3 \hat{i}} = \frac{4}{3}$

Which one of the above statement(s) is / are correct?

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Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 54

If

θ

is the angle between the vectors

4 (\hat{i} - \hat{k})

and

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

, then what is

(\sin θ + \cos θ)

equal to?

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Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 55

Which one of the following vectors are normal to the vector

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

?

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Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 56

If

|\vec{a}| = \sqrt{2}, |\vec{b}| = \sqrt{3}

and

|\vec{a} + \vec{b}| = \sqrt{6}

, then what is

| a - b |

equal to?

MEDIUM

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 30 - Vector Algebra>Practice Exercise>Q 57

If the magnitude of

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

equals to

\vec{a} \cdot \vec{b}

, then which one of the following is correct?