Question

If `|bara + barb| = |bara - barb|, bara` and `barb` are non-zero vectors, find the angle between `bara` and `barb`.

Answer 1

`|bara + barb| = |bara - barb|`

Squaring both sides

`(bara + barb) * (bara + barb) = (bara - barb) * (bara - barb)`

∴ `a^2 + 2bara * barb + b^2 = a^2 - 2bara * barb + b^2`

∴ `4bara * barb` = 0,

∴ `bara * barb` = 0

∴ `bara` is perpendicular to `barb`.

Hence angle between `bara` and `barb` is 90°.