Question

Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The cylinder x² + y² = 9 and the surface z = xy?

Answer 1

The vector function r(t) that represents the curve of intersection of the cylinder x² + y² = 9 and the surface z = xy is r(t) = xi + sqrt(9 - x²)j + (x*sqrt(9 - x²))k.

Step-by-step explanation:

To find the vector function r(t) that represents the curve of intersection of the two surfaces, we need to find the points where the cylinder and the surface intersect. Since the cylinder equation is x² + y² = 9 and the surface equation is z = xy, we can substitute y = sqrt(9 - x²) into the surface equation to get z = x*sqrt(9 - x²). Therefore, the vector function r(t) = xi + sqrt(9 - x²)j + (x*sqrt(9 - x²))k represents the curve of intersection of the two surfaces, where t is a parameter.