# Vector A=125 m/s, 40 degrees north of west. Vector B is 185 m/s, 30 degrees south of west and vector C is 175 m/s 50 east of south. How do you find A+B-C by vector resolution method?

##### 1 Answer

The resultant vector will be

#### Explanation:

First, you will resolve each vector (given here in standard form) into rectangular components (

Then, you will add together the

Finally, convert the resultant into standard form.

Here's how:

Resolve into rectangular components

Note that all given angles have been changed to standard angles (counterclockwise rotation from the

Now, add the one-dimensional components

and

#R_y = A_y+B_y-C_y = 80.35-92.50+112.49=100.34m/s

This is the resultant velocity in rectangular form. With a negative

Now, convert to standard form:

This angle looks a bit strange! Remember, the vector was stated to point into the second quadrant. Our calculator has lost track of this when we used the

To find this angle, add 180° to the (incorrect) result above. The angle we want is 165.6°.

If you get into the habit of always drawing a reasonably accurate diagram to go along with your vector addition, you will always catch this problem when it occurs.