If a- b- c- are vectors such that a-b-0 and a-b-c- thenA- - b -2- a -2- c -2B- None of theseC- -a-2-b-2-c-2D- - a -2- b -2- c -2

The correct option is C |a⃗|^2+|b⃗|^2=|c⃗|^2We have, a⃗+b⃗=c⃗ ⇒ |c⃗|^2=|a⃗|^2+|b⃗|^2+2 a⃗.b⃗ ⇒ |c⃗|^2=|a⃗|^2+|b⃗|^2+2 × 0 [∵a⃗.b⃗=0] ⇒ |c⃗|^2=|a⃗|^2+|b⃗|^2 ...

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Byju's Answer

Standard X

Mathematics

Applications of Dot Product

If a⃗, b⃗, c⃗...

Question

If $\to a, \to b, \to c$ are vectors such that $\to a . \to b = 0$ and $\to a + \to b = \to c$ , then

| \to a |^{2} + | \to b |^{2} = | \to c |^{2}

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| \to a |^{2} = | \to b |^{2} + | \to c |^{2}

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| \to b |^{2} + | \to a |^{2} = | \to c |^{2}

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Solution

The correct option is A $| \to a |^{2} + | \to b |^{2} = | \to c |^{2}$
We have, $\to a + \to b = \to c$
$\Rightarrow | \to c |^{2} = | \to a |^{2} + | \to b |^{2} + 2 \to a . \to b \Rightarrow | \to c |^{2} = | \to a |^{2} + | \to b |^{2} + 2 \times 0 [∵ \to a . \to b = 0] \Rightarrow | \to c |^{2} = | \to a |^{2} + | \to b |^{2}$

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