 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/11/b/i/solution

Take the cross product with

c

. Since

c \times c = 0

, the equation implies

x \times c = a \times c, (x - a) \times c = 0.

c \neq = 0

, the displacement is parallel to

c

. Therefore

x = a + λ c, λ \in R .

This is a necessary condition; substitution must still determine which points on this straight line satisfy the full equation.

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