 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/11/a/solution

Equating the three Cartesian components gives

2 + λ = - μ, - 1 + λ = 6 + 2 μ, λ = 4 + μ .

The first and third equations yield

λ + μ = - 2

and

λ - μ = 4

, hence

λ = 1

μ = - 3

. They also satisfy the middle equation, so the intersection is

λ = 1, μ = - 3, p = (3, 0, 1) .

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