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Vector Triple Product

If PS QR an...

Question

If $P S ⊥ Q R$ and $P Q = a, P R = b, Q S = c, P R = b$ and $R S = d,$ then prove that $(a + b) (a - b) = (c + d) (c - d)$

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Solution

REF.Image
$Q R = a^{2} - b^{2}$
also,
$Q R = c^{2} - d^{2}$
$∴ a^{2} - b^{2} = c^{2} - d^{2}$
$(a - b) (a + b) = (c - d) (c + d)$

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