Finding the magnitude and direction of a vector ?

Question

Find the vector sum A+B:

Vector A has a magnitude of 7 and is going due west

Vector B has a magnitude of 20 and is going 37 degrees north of east

I know what the answer should be, but I can't get it to come out right? Any help?

Answer 1

Draw A, then draw B starting from the tail of A.  The line that then connects the start of A to the tail of B is the line you're looking for.  That's how you can add graphically.  Draw it, and it'll make sense.

One way to find the numerical answer of the resultant vector is to separate both vectors into components.  

So A is -7 in the x direction for example.  That's its only component.  B is 20cos(37) = 16 in the x direction, and 20sin(37) = 12 in the y direction.  Add the components.

That gives you 9 in the x, and 12 in the y.  Draw those lines as two lines in a right triangle, and the hypotenuse is the vector length (in this case 15).  

Then to find the angle, you do tan^-1(y/x) = tan^-1(12/9) = 53 degrees.  In your case, it's 53 degrees north of east because of the signs of x and y.  

15  going 53 degrees NE

Hope that helps.