Let d(u,v) be the distance between two vectors u and v in R2. We want to show that d(u,v) = 0 if, and only if, u = v. Do this in two steps: (a)...

6. Let d(u,v) be the distance between two vectors u and v in R2. We want to show that d(u,v) = 0 if, and only if, u = v. Do this in two steps:

(a) Carefully show that if u = v, then d(u,v) = 0. (b) Show that if d(u,v) = 0, then u = v.

7. A lawnmower has a mass of 25 kg. It is being pushed with a force of 90 N in the direction of the handle. If the handle makes an angle of 45◦ with the ground, what is the horizontal component of the force that is causing the mower to move forward?