 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2021/4/solution

At their intersection,

x^{2} + y^{2} = 1

and

z^{2} = 1

n_{s} = (2 x, 2 y, 2 z), n_{c} = (2 x, 2 y, 0) .

The acute angle between the tangent planes is the acute angle between these normal vectors. Their dot product gives

cos α = \frac{∣ n _{s} \cdot n _{c} ∣}{∣ n _{s} ∣ ∣ n _{c} ∣} = \frac{4}{( 2 2 ) ( 2 )} = \frac{1}{2}, α = \frac{π}{4} = 4 5^{\circ} .

It is the same at every intersection point; the supplementary oriented angle is

13 5^{\circ}

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