Math Help - Can someone help me w/ Vectors? plz?

1. Can someone help me w/ Vectors? plz?

Im having trouble of doing these problems. I dont really know the steps of how you do them. So if someone could help me Id really appreciate it.
Ive scanned the problems from my math book so if anyone could help that beeee soo great!!
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2. you're missing the sign of the j component for the vector r

3. Hello, takkun0486!

Here's #2 . . .

2. A ship sails for 25 miles on a bearing of 225°,
then turns and sails on a bearing of 300° for 16 more miles.

a) How far is the ship from its starting point?

b) At what bearing does the ship end up with respect to where it started?
A sketch is always welcome.
Code:
                                | A
*
b       *   * |
*       *45°|
*           *     |
C *       :       *       |
*     :     * c=25    |
a=16 *60°:45°*           |
* : *
*
B

The ship starts at A, sails southwest for 25 miles to point B.
Then heads 60° west of north for another 16 miles to point C.

a) We want side b = AC.

Law of Cosines: . .= .16² + 25² - 2(16)(25)cos105° .= .1088.066236

Therefore: .b . .33 miles.

b) We want angle A.
. . . . . . . . . . . . . . . . . . . .b² + c² - a² . . . 33² + 25² - 16²
Law of Cosines: . cos A .= .--------------- .= .------------------- .= .0.883636364
. . . . . . . . . . . . . . . . . . . . . . 2bc . . . . . . . . .2(33)(25)

Hence: .A . .28°

Therefore, the ship is at a bearing of: .225° + 28° .= .253°