A vector with magnitude 7 points in a direction 325 degrees counterclockwise from the positive x axis.

Answer 1

325 clockwise is a reference angle of 360-325 = 35 degrees

use a calculator with a trig function

tan 35 degrees = about 0.7002075 = about .7

sin35 = .57

cos 35 = .82

magnitude = 7 = hypotenuse of a right triangle with opposite side = 7sin35 = 7(.57) = about 3.9 = y

adjacent side = 7cos35 = 7(.82) = about 5.7 = x

polar coordinates (7, 35) or (7,0.19pi)

rectangular coordinates (x,y) = (5.7, 3.9)

vector <5.7, 3.9>

it's a directed line segment from the origin to the point (5.7,3.9)

but you want counterclockswise

that vector is to the point (5.7,-3.9)

<5.7,-3.9>

the vector is "just" a magnitude and direction, it's moveable

it's the same whether it's from the origin to (.57,-3.9) or from two other points with the same direction and magnitude such as from (.57,-3.9) to (1.14, -7.8)

any two points with a line segment through them with the same slope and same length have the same vector