# Given Vector A: 25.2cm at 81.6 degrees and Vector B: 32.1 cm at 142.7 degrees. How do you add and subtract these two vectors?

##### 1 Answer

You will need to convert both vectors into rectangular components (

#### Explanation:

This is a problem in two-dimensional vector addition.

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

Now, to add the two vectors, you add the one-dimensional components

(If you want to subtract the second vector from the first, you would subtract the components at this stage instead.)

and

This is the resultant vector 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 116.1°.

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.