Can someone PLEASE help with this physics questions?

Question

 The figure shows two vectors B and C, along with their magnitudes and directions. The vector D is given by D = B - C 

A) What is the magnitude of vector D? 

B) What angle does vector D make with the +x axis (give the angle between 0o and 360o)? 

THANKS SO MUCH

Answer 1

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B-C = B +(-C) so picture the arrow C reversed in direction and added to B.  You should draw this.  Mathematically you calculate the x components and the y components.

Dx = 6 sin(53) + 4 cos(32)

Dy = 6 cos(53) + 4 sin(32)

Now combine them using Pythagoras' theory.  D = sqrt( Dx^2+Dy^2)

To get the angle you will note that it is down and to the left.  The angle from the x axis is found by tan(theta) = Dy/Dx  ie theta = atan(Dy/Dx)