Exercises: Vectors

Exercise 1:    Suppose that the vector A is in standard position in the coordinate plane having terminal point (5, -9).  Use Mathematica to find the magnitude of A and the angle that A makes with the horizontal.

Exercise 2:    Given the vector A in standard position in 2-dimensional space having length 8 units and direction 25° with respect to the horizontal, use Mathematica to find the coordinates of the terminal point (A_x, A_y) of A.

Exercise 3:    Let A be the vector (1, -3, 2, -4, 5, 4) and let B be the vector (-3, -2, 7, -1, 2, -3).  Find each of the following:
a)    2 A
b)    -4 B
c)    A + B
d)    B - A
e)    3 A + 4 B
f)    2 B - 3 A
g)    A · A
h)    B · B
i)    A · B