Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 + y2 = 16 and the surface z = xy

A vector function r(t) is represented as:

The vector function r(t) that represents the intersection of the two surfaces is  

Given

Express 16 as in

Multiply by 1

In trigonometry

So, we substitute for 1

Remove bracket

Apply law of indices

By comparison:

and

Take positive square roots

and

Recall that:

So, we have:

Substitute the values of x, y and z.

Hence, the vector function r(t) is:

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