1) Suppose a and b are two vectors that start from the same initial point. If |a| = 8 and |b| = 11, and they form a triangle with an area 32 square units: a. What is the angle between a and b? b. What is the scalar projection of a onto b? c. What is the vector projection of a onto b?

Assume that the coordinates of the points P, Q, R, S, and O are as follows: P(-3, 2) Q(6, 4) R(4, 3) S(5, 9) O(0, 0) Draw the indicated vector and compute its magnitude. Upload your handwritten answer on Canvas. PQ

1. Consider the vectors = (2, 1) and w = (-2,3) (a) Sketch a graph of the vectors and w in the space provided below. Label both vectors. Number the axes so that the vector coordinates can be read from the axes. (b) Compute the dot product and the magnitudes || and |w|. Use this to find the angle between the vectors and w. Include the units used for the angle.

2. Find the angle between the following two vectors. and