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Addition of Vectors

The vectors b...

Question

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

$4 \sqrt{2}$ , 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, $\to b ⊥ \to c, ∴ \to b \cdot \to c = 0$
Now, $\to d = \to c - \to b$ $\Rightarrow | \to d |^{2} = | \to c - \to b |^{2}$
$= | \to c |^{2} + | \to b |^{2} - 2 \to b \cdot \to c = 16 + 16 - 0$
$\Rightarrow | \to d | = \sqrt{32} = 4 \sqrt{2}$
Now the direction of $\to b$ is north east so the direction of $- \to b$ will be south west
and since the magnitude of vectors $\to b$ and $\to c$ is equal $\to d$ will lie in the direction of angle bisector of $- \to b$ and $\to c$ so the direction of $\to d$ is west.

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