If the vectors \( -3 i+4 j+\lambda k \) and \( \mu i+8 j+6 k \) are co

1.	If the vectors \( -3 i+4 j+\lambda k \) and \( \mu i+8 j+6 k \) are collinear vectors, then find \( \lambda \) and \( \mu \).
Answer» 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

If the vectors \( -3 i+4 j+\lambda k \) and \( \mu i+8 j+6 k \) are collinear vectors, then find \( \lambda \) and \( \mu \).

Answer»

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

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If the vectors \( -3 i+4 j+\lambda k \) and \( \mu i+8 j+6 k \) are collinear vectors, then find \( \lambda \) and \( \mu \).

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