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Byju's Answer

Standard IX

Mathematics

Addition of vectors

The vectors b...

Question

The vectors b and c are in the direction of north-east and north-west respectively and $| b | = | c | = 4$ . The magnitude and direction of the vector d = c - b, are

4 $\sqrt{2}$ , towards north

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4 $\sqrt{2}$ , towards west

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4, towards east

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4, towards south

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Solution

The correct option is B
4 $\sqrt{2}$ , towards west

Clearly, $b ⊥ c, ∴ b . c = 0$
Now, d = c - d $\Rightarrow | d |^{2} = | c - b |^{2}$
$= | c |^{2} + | b |^{2} - 2 b . c = 16 + 16 - 0$
$\Rightarrow | d | = \sqrt{32} = 4 \sqrt{2}$ and direction of d is west.

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The vectors b and c are in the direction of north-east and north-west respectively and $| b | = | c | = 4$ . The magnitude and direction of the vector d = c - b, are

The correct option is B
4 $\sqrt{2}$ , towards west

Clearly, $b ⊥ c, ∴ b . c = 0$
Now, d = c - d $\Rightarrow | d |^{2} = | c - b |^{2}$
$= | c |^{2} + | b |^{2} - 2 b . c = 16 + 16 - 0$
$\Rightarrow | d | = \sqrt{32} = 4 \sqrt{2}$ and direction of d is west.