 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/11/b/solution

The plane normals are

n_{1} = (2, - 1, - 1)

and

n_{2} = (3, - 1, - 3)

(2, 3, 1)

, perpendicular to both normals and hence parallel to the intersection line. Setting

z = 0

in both equations gives the common point

(1, - 1, 0)

. Therefore

r = (1, - 1, 0) + t (2, 3, 1), t \in R .

The normals are not parallel, so their intersection is a unique line.

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