Here are two vectors: a = (4.0m)i - (3.0m)j and b = (6.0m)i + (8.0m)j?

Question

Here are two vectors:
a = (4.0m)i - (3.0m)j and b = (6.0m)i + (8.0m)j

What are (a) the maginitude and (b) the angle (relative to i) of a? What are (c) the magnitude and (d) the angle of b?
What are (e) the magnitude and (f) the angel of a + b; (g) the magnitude and (h) the angle of b - a; and (i) the magnitude and (j) the angle of a - b? (k) What is the angle between the directions of b - a and a - b?

Answer 1

Just substitute i and j for x and y on a graph since there's no k (z) component.
4i by -3j gives (graphically) 4m right by 3m down...vector resultant is 5m at 36.87 degrees below x axis.

6i by 8j gives 6m right by 8m up...vector is 10m at 62.13 degrees above x axis.

divergence angle of a and b is 90 degrees.

a + b = 10i + 5j
b - a = 2i + 11j
a - b = -2i - 11j

A little pythagorean theorem & trig and you have it.