 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/1/b/solution

Equating Cartesian components gives

1 - s = t

- s = - 1 + t

, and

2 + s = 2 t

. Substitution of

t = 1 - s

into the last equation gives

s = 0

, hence

t = 1

. Both parametrizations therefore give the intersection point

r = (1, 0, 2) .

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