 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/11/d/iv/solution

c = p \times \hat{a}

is a normal vector to the span of

p

and

\hat{a}

. Since

c \neq = 0

, these vectors determine a plane. Thus the missing words are

the line and the origin.

Indeed this plane consists of all linear combinations of

p

and the line's direction vector.

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