1. Consider the two surfaces defined by the following equations: y = 2x z = x + y (a) (2 points) Find a parametric equation r(t) to parameterise the curve at the intersection of these two surfaces. (b) (2 points) Sketch the "shadow" that this curve would cast into the ry and xz planes (i.e. ignore the z coordinate and then ignore the y coordinate) (c) (2 points) Compute the tangent vector r'(t) (d) (2 points) What is the speed when t = 1? (e) (2 points) What is a parametric equation for the tangent line when t = 1? (f) (2 points) Set up an integral for the arc-length over the interval [0, 1]. Do not evaluate the integral.