Question

If the two vectors `3hati + αhatj + hatk` and `2hati - hatj + 8hatk` are perpendicular to each other, then find the value of α.

Answer 1

`veca = 3hati + αhatj + hatk`

and `vecb = 2hati - hatj + 8hatk`

∵ `veca` and `vecb` are perpendicular.

∴ `veca*vecb` = 0

(3)(2) + α(–1) + 1 × 8 = 0

6 – α + 8 = 0

`\implies` α = 14