If two lines L1 and L2 in space, are defined by L1 = {x = √λ y + (√λ − 1), z = (√λ − 1)y + √λ} and L2 = {x = √μ y + (1 − √μ), z = (1 − √μ)y + √μ} then L1 is perpendicular to L2, for all nonnegative reals λ and μ, such that:

Question

Accepted Answer

λ = μ. The lines L1 and L2 are defined in a way that their direction vectors depend on the parameters λ and μ. When λ equals μ, the direction vectors become proportional, ensuring that the lines are perpendicular to each other, as their slopes will satisfy the condition for perpendicularity in three-dimensional space.

If two lines L1 and L2 in space, are defined by L1 = {x = √λ y + (√λ − 1), z = (√λ − 1)y + √λ} and L2 = {x = √μ y + (1 − √μ), z = (1 − √μ)y + √μ} then L1 is perpendicular to L2, for all nonnegative reals λ and μ, such that:

Solution

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