Question

Consider the lines ℓ1 = { (−1 + 2t, t, α − t) |t ∈ R}...

Consider the lines ℓ1 = { (−1 + 2t, t, α − t) |t ∈ R} and ℓ2 = { (2s, α + s, 3s) | s ∈ R }.

(a) There is only one real value for the unknown α such that the lines ℓ1 and ℓ2 intersects each other at a point P ∈ R^3 . Calculate that value for α and determine the point P.

(b) If α = 0, is there a plane π ⊂ R^3 containing both lines ℓ1 and ℓ2? Justify your answer.

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Answer #1

Convert both the lines from parametric form to general form and use the properties of line and plane.

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