Question

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

Answer 1

We have

\(|\vec a| = \sqrt{1^2 + (-2)^2 + 3^2}\)

\(= \sqrt {14}\)

Now square both sides \(|\vec a - \vec b| = \sqrt 7\)

⇒ \(|\vec a| ^2 + |\vec b|^2 - 2\vec a . \vec b = 7\)

⇒ \(14 + |\vec b|^2 - 2|\vec b|^2 = 7\),  [using the given condition]

⇒ \(|\vec b|^2 = 14 - 7 = 7\)

⇒ \(|\vec b| = \sqrt 7\)