# Solving vectors using component method

by yety124
Tags: component, method, solving, vectors
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,568 Solving vectors using component method If $\theta$ is measured counterclockwise from the positive x-axis then a vector of length r and angle $\theta$ has components $rcos(\theta)$ and $r sin(\theta)$. Strictly speaking, you are free to choose the "positive x-axis" any way you want as long as you are consistent but the usual convention is that the positive x-axis points East. For the first vector you are given that r= 175km and the directon is 30 degrees north of east. "north of east" is counterclockwise from east so the angle is $\theta= 30$ degrees. For the second vector you are given that r= 153km and the direction is 20 degrees west of north. West is clockwise of north but north itself is 90 degrees clockwise of east. The angle is $\theta= 90+20= 110$ degrees. For the third vector you are given that r= 195km and the direction is west. West is exactly opposite east so the angle is $\theta= 180$ degrees.