Question

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

Answer 1

The vector function that represents the curve of intersection between the cylinders x² + y² = 16 and the surface z = xy is r(t) = (4cos(t), 4sin(t), 4cos(t)*4sin(t)).

Step-by-step explanation:

To find a vector function that represents the curve of intersection between the cylinders x² + y² = 16 and the surface z = xy, we need to express the curve in terms of a parameter t. We can do this by substituting x = 4cos(t) and y = 4sin(t) into the equation of the surface. This gives us the vector function r(t) = (4cos(t), 4sin(t), 4cos(t)*4sin(t)).