The vectors (A + B) and (A - B) are at right | vedclass

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Question

(A) Given that the vectors $(A + B)$ and $(A - B)$ are at right angles to each other,their dot product must be zero.$(A + B) \cdot (A - B) = 0$Expandi

Vedclass · Accepted Answer

$|A|=|B|$

Vedclass · Answer

(A) Given that the vectors $(A + B)$ and $(A - B)$ are at right angles to each other,their dot product must be zero.$(A + B) \cdot (A - B) = 0$Expanding the dot product:$A \cdot A - A \cdot B + B \cdot A - B \cdot B = 0$Since the dot product is commutative $(A \cdot B = B \cdot A)$,the terms $-A \cdot B$ and $B \cdot A$ cancel out.$|A|^2 - |B|^2 = 0$$|A|^2 = |B|^2$Taking the square root on both sides,we get:$|A| = |B|$Thus,the condition is that the magnitudes of the two vectors must be equal.

The vectors $(A + B)$ and $(A - B)$ are at right angles to each other. This is possible under the condition

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