Question

Find λ and μ if  `(2hati + 6hatj + 27hatk) xx (hati + lambdahatj + muhatk) = vec0`.

Answer 1

Let `veca = 2 hati + 6hatj + 27hatk` and `vecb = hati + lambda hatj +muhatk .`

∴ ` (veca xx vec b) = |(hati, hatj, hatk), (2, 6, 27), (1, lambda, mu)|`

`= hati (6mu - 27 lambda) - hatj (2mu - 27) + hatk (2lambda - 6)`

`= (6mu - 27 lambda) hati + (27 - 2mu) hatj + (2 lambda - 6) hatk`

By the question, `veca xx vecb = vec0`

⇒ `(6mu - 27 lambda) hati + (27 - 2mu) hatj + (2 lambda - 6) hatk = vec0`

⇒ `6 mu - 27 lambda = 0, (2 lambda - 6) = 0, (27 - 2 mu) = 0`

⇒ `lambda = 3`

and `mu = 27/2.`