 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2021-resit/3/b/solution

A parallel plane has the same normal vector, so write

C : x + 2 y - 4 z = d

. Substitution of the given point gives

d = 4 + 4 - 4 = 4

. Thus

C : x + 2 y - 4 z = 4.

A displacement between the two planes has a component of magnitude

∣5 - 4∣/∥ n_{A} ∥

along their common unit vector normal. The distance between parallel planes is consequently

dist (A, C) = \frac{1}{21} .

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