Question

If the plan 2 X + 4 Y + 3Z = 5 and X + 2 Y + Lambda Z = 12 are perpendicular to each other find the value of Lambda

Answer 1

As per the question,

2x + 4y + 3z = 5 and x + 2y + λz = 12 are perpendicular.

We can conclude that their normals will also be perpendicular.

n₁ = (2, 4, 3) and n₂ = (1, 2, λ)
so, n₁ . n₂ = 0

2x1 + 4x2 + 3xλ = 0
2 + 8 + 3λ = 0
λ = -10/3