Question

Given 2 vectors `A = 4.00i + 3.00j` and `B =5.00i - 2.00 j` how do you find the magnitude & direction of the vector difference A - B?

Answer 1

We can subtract directly the corresponding components and check using the parallelogram rule.

Explanation:

Have a look:

Where, graphically, I used the fact that:
`vecA-vecB=vecA+(-vecB)`

For the magnitude we use Pythagoras (with the components) to get:
`|vecA-vecB|=sqrt((-1)^2+(5)^2)=sqrt(1+25)=sqrt(26)~~5.1`

For the direction I can see that will be `90^@` from the `x` axis up to the `y` axis, plus the little bit passed the `y` axis given as:
`theta=arctan(1/5)=11.3^@`
giving in total: angle`=90^@+11.3^@=101.3^@`