Vector problem?

Question

How do i find the magnitude and direction of the difference vector A - B.

How do i find the magnitude and direction of the difference vector B - A.

Vector A- a displacement of 20m due east

Vector B- a displacement of 30m due north

Answer 1

Vector subtraction is simple, just subtract the components of the vector to get the direction and the magnitude is just subtraction of the magnitudes (mag of A-B is 10m, B-A is also 10m, direction of A-B is due west, direction of B-A is north)

Answer 2

1) If you again must use the graphical method, then make A negative by making it the opposite direction.

A becomes 20m due west

You end up with a right angled triangle.

a² = b² + c²

a² = 30² + 20²

a = 36 m

Now find the direction:

tan x = 20 / 30

x = 33.7 degrees

Therefore the resultant displacement is

36 m [33.7 degrees W of N]

2)

Make B negative this time.

B becomes 30 m due south.

The displacement's magnitude will be the same, 36 m.

Find the angle:

tan x = 30 / 20

x = 56.3 degrees

Therefore the resultant displacement is

36m [56.3 degrees S of W]