2. (4 points) A swimmer plans to swim across a river that is 2 mile wide, aiming to land at a point 1 mile upstream from her starting point. She can swim at a constant speed of 1.5 miles per hour. The current in the river flows at 0.5 mile per hour downstream. (a) In order to swim in a straight line to reach her destination, in what direction should she steer? (b) How long will the trip take? 1 mile destination 2 miles direction of current origin5. (4 points) Find equations for the following planes [a] the plane that passes through the point (1, 1, 1) and contains the line with symmetric equations a: = 23,: = 32'. (b) the plane that contains all points that are equidistant from the points (3, 2, 1) and (7, 4, 3). 7. (4 points) (a) Find the distance between the two parallel planes: 2;: + y 3: = 4 and 433+2yz=2. (1')) Suppose that In - r = a. and n - r = 13 describe two parallel planes. Derive a formula for the distance between them. Your answer will be in terms of InI 11I a, b. 9. (3 points) Find an equation for the surface consisting of all points P for which the distance from P to the y-axis is half the distance from P to the ass-plane. Identify the surface. 10. (3 points) Show that the curve with parametric equations :3 = sin{t), y = cos{t), z = sin2(t) is the curve of intersection of the surfaces 2 = 9:2 and 3:2 + y2 = 11. (4 points) (a) Find the point on the curve r(t) = (t3 +3t,t3 + mm + 2:3), 0 g: t <_: where the tangent line is parallel orthogonal to plane find equation of curve r at point you found in part points what on i="t3," y="3t," z="f31" normal by show that if position vector rft always perpendicular velocityr then lies entirer a sphere centered origin>