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Work Done as Dot Product

Two vectors ...

Question

Two vectors $\to A$ and $\to B$ such that $(\to A + \to B) ⊥ (\to A - \to B)$ . Then,

A

\to A | | \to B

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B

\to A ⊥ \to B

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C

| \to A | = | \to B |

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D

| \to A | \neq | \to B |

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Solution

The correct option is D $| \to A | = | \to B |$
Vectors are perpendicular to each other, so their dot product is zero:
$(\to A + \to B) \cdot (\to A - \to B) = 0 A^{2} - \to A \cdot \to B + \to B \cdot \to A - B^{2} = 0 o r A^{2} - B^{2} = 0 ∣ ∣ \to A ∣ ∣ = ∣ ∣ \to B ∣ ∣$

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