If - a - b - a - b - then which of the following options is correct-A- a bB- a - bC- a and b are antiparallelD- a and b are inclined at angle of 60-

The correct option is B a⊥bWe have|a×b|^2 = (a + b).(a + b) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp;=a.a+a.b+ b ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If | a + b |=...

Question

If $| \to a + \to b | = | \to a - \to b |$ , then which of the following options is correct?

\to a ⊥ \to b

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\to a | | \to b

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\to a and \to b are antiparallel

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\to a and \to b are inclined at angle of 60^{\circ}

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Solution

The correct option is A $\to a ⊥ \to b$
We have $| \to a \times \to b |^{2} = (\to a + \to b) . (\to a + \to b)$
$= \to a . \to a + \to a . \to b + \to b . \to a + \to b . \to b$
$= a^{2} + b^{2} + 2 \to a . \to b$
Similarly,
$| \to a - \to b |^{2} = (\to a - \to b) . (\to a - \to b)$
$= a^{2} + b^{2} - 2 \to a . \to b$
$If | \to a + \to b | = | \to a - \to b |$
$a^{2} + b^{2} + 2 \to a . \to b = a^{2} + b^{2} - 2 \to a . \to b$
$\Rightarrow \to a . \to b = 0 \Rightarrow \to a ⊥ \to b$

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If |→a+→b|=|→a−→b|, then which of the following options is correct?

If $| \to a + \to b | = | \to a - \to b |$ , then which of the following options is correct?