Question

If the vectors -3i + 4j + λk and μi + 8j + 6k are collinear vectors, then find λ and μ.

Answer 1

Answer : ⇒   μ = - 6        And     λ =   3

Given that

⇒ the vectors -3i + 4j + λk and μi + 8j + 6k are collinear vectors.

Collinear means the vectors lying on the Same Line.

So the vectors can be

• Parallel
• Anti-parallel

In both cases, the ratio of their respective components will be Equal.

So we have

                        -3i + 4j + λk    &

                         μi + 8j + 6k

Comparing both, we get

       -3/μ = 4/8 = λ/6

        -3/μ = 1/2 = λ/6

⇒  -3/μ = 1/2   And   1/2 = λ/6

⇒  μ/-3 = 2/1   And   λ/6 = 1/2

⇒   μ = -3(2)     And     λ = 6(1/2)

⇒   μ = - 6        And     λ =   3