Question

The sum of two vector A and B is 5i+j and their difference is 3i-2j the vector then is?

Answer 1

The vectora are `vecA=(4hati-1/2hatj)` and `vecB=(hati+3/2hatj)`

Explanation:

The sum is

`vecA+vecB=5hati+1hatj`

The difference is

`vecA-vecB=3hati-2hatj`

Adding the `2` equations

`2vecA=8hati-1hatj`

`vecA=1/2(8hati-1hatj)=4hati-1/2hatj`

Subtracting the `2` equations

`2vecB=2hati+3hatj`

`vecB=1/2(2hati+3hatj)=hati+3/2hatj`