Question

If `2hati + 3hatj, hati + hatj + hatk` and `λhati + 4hatj + 2hatk` taken in order are coterminous edges of a parallelopiped of volume 2 cu. units, then find the value of λ.

Answer 1

Let `bara = 2hati + 3hatj, barb = hati + hatj + hatk, barc = λhati + 4hatj + 2hatk`

 Volume of parallelepiped = `[(bara, barb, barc)]`

∴ 2 = `|(2, 3, 0),(1, 1, 1),(λ, 4, 2)|`

∴ 2 = 2(–2) – 3(2 – λ)

∴ 2 = – 4 – 6 + 3λ

∴ 12 = 3λ

∴ λ = 4