# Math Help - vector resultant

1. ## vector resultant

find the magnitude and direction of the resultant of two vectors u and v with magnitudes of 6 and 2 and an angle of 140 between them.

i got |u+v|=7.64 units and the direction to be 9.69 deg, is it right?

2. You can make a sketch, and complete the parallelogram of forces.

From this, the magnitude of the resultant forces is given by the cosine rule, taking the sides 6 and 2 and the angle (180-140) = 40 degrees.

$Resultant = \sqrt{2^2 + 6^2 - 2(2)(6)\cos(40)}$

Can you try out again on the direction now?

3. i get 4.64 units and 16 deg

4. That's it!

Well done.

Here's a picture to see where the 40 degrees came from: