TVec11 A vector has an x component of –20 and a y component of 32. Find the magnitude and direction of the vector.

First sketch the components on a coordinate system.

Now draw in the resultant and the angle.

The angle shown is from

Notice that the principle angle was used. You could have used - 20 over 32 to get 122^o, but drawing the picture and using the principle angle is the beter way to avoid making mistakes with signs.

The magnitude is

Remember that the direction has to be measured from the positive x axis so the vector is written as