# If #A= <3, -1 ># and #B= <-8, 6>#, what is #||A+B|| -||A|| -||B||#?

##### 1 Answer

We find the length of the resultant vector from adding two vectors together and then subtract from it the length of the two component vectors.

#### Explanation:

We are effectively finding the length of the new vectors that is the sum of two vectors, minus the lengths of each of the component vectors.

If you draw a diagram you will see why we expect the answer to be negative: the resultant vector is shorter than the two vectors that make it up (unless those two vectors are in the same direction).

First step is to add the vectors:

Second is to find the lengths of each of the three vectors we're interested in:

Pulling it all together,

As we predicted, the answer is negative.