# Math Help - vectors

1. ## vectors

Find the resultant of the following vectors:
a) 50 units due east and b) 100 units 30 degrees north of west.

the resultant can be found by using the law of cosines. however, i don't understand why you change the addition sign to the subtraction sign to get the correct answer:

by not changing the formula you get:
R^2 = a^2 + b^2 - 2ab*cos(angle)
R^2 = 100^2 + 50^2 - 2(100)(50)(cos150) = 145 units

by changing the sign you get:
R^2 = a^2 + b^2 + 2ab*cos(angle)
R^2 = 100^2 + 50^2 + 2(100)(50)(cos150) = 62 units

62 units is the correct answer, but i do not understand why the sign must be changed?

2. the angle should be 30 degrees ...

$R = \sqrt{100^2 + 50^2 - 2(100)(50)\cos(30)}
$