Determine the magnitude of the vector sum v = v1 + v2 and the angle θx which v makes with the positive x-axis. complete both graphical and algebraic solutions.

Let  θ be the angle V1 makes with x axis and θ2

√√√To start, we have  

Tan θ = 3/6=1/2

From there, do some quick manipulation to find sin θ1 and cosθ1  

So we have v1= (9 cos θ1and 9 sin θ1)=(8.05,4.02)

Now, v2 makes an angle of 1800- 630=1170=θ2with x axis so we have  

V2=(12 cosθ2,12sinθ2)=(-5.45,10.69)

From there, we have  

V=v1+v2=(2.60,14.71)

Now it’s a simply a matter of finding /v/=  √2.602+14.712

=14.9

Θx=arctan(14.71/2.6)=80°