If $a = i + 2 j - 3 k, b = 3 i - j + 2 k$ then show that $a + b, a - b$ are mutually perpendicular.

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Solution

We have
$\to a = ˆ i + 2 ˆ j - 3 ˆ k$

$\to b = 3 ˆ i - ˆ j + 2 ˆ k$

$∴ \to a + \to b = 4 ˆ i + ˆ j - ˆ k$
$\to a - \to b = - 2 ˆ i + 3 ˆ j - 5 ˆ k$
Then
$(\to a + \to b) . (\to a - \to b) = - 8 + 3 + 5 = 0$
Hence,
$∴ (\to a + \to b) ⊥ (\to a - \to b)$
Proved.

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