Determine whether the following statements are True or False. 1 point each. In the following problems, V is always vectors and p, q are always points.

(a) Determine whether the following statements are True or False. 1 point each. In the following problems, V is always vectors and p, q are always points. i . The object V + p is a point. ii. The object V + W is a point. iii The object p - q is a point. iv . Let p be on the unit circle. Then p x q is a point in the plane that can be thought of as q being rotated by the angle determined by p around the origin. V . If tan 0 = 2, then | | (cos 0, sin 0) |1 - 2. vi. If V = p - q then -V = q - p. vii. The vectors V, 2V and 5V all have the same direction. viii. Since cos() = 0, there are some situations in which rotating a line segment will compress it into a single point since the equation gets multiplied by 0. (b) An arc is drawn along a unit circle of length 3. i. What is the angle measure of this arc in radians? ii. Given that 7 ~ 3.14, does this arc cover an angle less than 180 degrees or more than 180 degrees? Why