http://www.ck12.org Chapter 7. Vectors
When you see this picture, it turns into a basic trig question to find thexandycomponents of the vector. Note that
the reference angle that the vector makes with the negative portion of thexaxis is 67. 5 ◦.
sin 67. 5 ◦= 17 y,cos 67. 5 ◦= 17 x
<x,y>≈<− 6. 5 , 15. 7 >Example B
A car driving 40 mph brakes and turns around a corner. Draw the approximate force vectors acting on the car as if
you were looking down on a map.
Solution: The primary force is the car’s inertia. This is the force acting on the car to keep it moving forward in a
straight line. There are three other forces that affect the car. First is gravity, but since this vector is perpendicular to
the other vectors it would require a third dimension which will not be considered at this time. The second force is
the brakes that act to slow the car down. This force is not as strong as the inertia force. The third force is the act of
turning which nudges the front portion of the car to one side. The picture below shows a sketch of the forces acting
on the car.
Example C
Consider the points:A( 1 , 3 ),B(− 4 ,− 6 ),C( 5 ,− 13 ). Find the vectors in component form of−→AB,−→BA,−→AC,CB−→.
Solution: Remember that when finding the vector between two points, start with the terminal point and subtract the
initial point.