Question 2 The direction of a vector is defined as the angle of the vector in relation to a horizontal line. As a standard, this angle is measured counterclockwise from the positive x-axis. The direction or angle of in the diagram is α.

Part A

How can you use trigonometric ratios to calculate the direction α of a general vector v = , similar to the diagram?

Part B

Suppose that vector V lies in quadrant II, quadrant III, or quadrant IV. How can you use trigonometric ratios to calculate the direction (i. e., angle) of the vector in each of these quadrants with respect to the positive x-axis? The angle between the vector and the positive x-axis will be greater than 90 degrees in each case.

Part C

Now try a numerical problem. What is the direction of the vector w = ?