If the vectors −3i + 4 j + λk and μ i + 8 j + 6k are collinear vectors then find λand μ.

Let a = −3 i + 4 j + λk , b = μ i + 8 j + 6k
From hyp. a, b are collinear then
a = tb
⇒ −3i + 4 j + λk = t(μ i + 8 j + 6k)
−3i + 4 j + λk = μt i + 8t j + 6tk
Comparing i, j, k coefficients on both sides
3
3
μt = −3 ⇒ μ = − = −
= −6 ⇒ μ = −6
t
1/ 2
4
1
8t − 4 ⇒ t = ⇒ t =
8
2
1
6t = λ ⇒ λ = 6 ⋅ ⇒ λ = 3