 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/1/a/solution

The direction vectors are

u = (1, - 2, 1)

and

v = (0, - 2, 1)

(0, - 1, - 2)

, with norm

5

. A unit normal to the plane is therefore

n = \frac{( 0 , 1 , 2 )}{5}, or its negative .

The two intersecting directions span the plane, so a vector orthogonal to both is a normal vector to that plane.

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