Hello again, John 5!

2.) Given two vectors:

$\displaystyle \vec{A}$, which has a length of 10.0 and makes an angle of 45° below the x-axis,

and $\displaystyle \vec{B}$, which has an x-component of +2.0 and y-component of +4.0.

(a) Sketch the vectors on x-y axes, with all their "tails" starting at the origin.

(b) Calculate $\displaystyle \vec{A} + \vec{B}$ Code:

| B
| * (2,4)
| /:
| / :
|/ :
O * - + - - + - -
| \ 45° :
| \ :
| 10 \ :
| \ :
| * A

We have: .$\displaystyle \vec{A} \;=\;\overrightarrow{OA} \;=\;\langle5\sqrt{2},\,\text{-}5\sqrt{2}\rangle$

. . , ,and: .$\displaystyle \vec{B} \;=\;\overrightarrow{OB} \;=\;\langle 2,\,4\rangle$

Therefore: .$\displaystyle A + B \;=\;\langle2 + 5\sqrt{2},\:4-5\sqrt{2}\rangle$