 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/1/solution

The

z

component of the cross product is

2 a - 2

. For the result to lie in the

x

y

plane, it must vanish, giving

a = 1

. The dot product condition is then

2 a + 2 - 3 b = 0

, so

a = 1, b = \frac{4}{3} .

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