Answer:
0.149 m, [tex]321.8^{\circ}[/tex]
Explanation:
Let's start by resolving each vector into its components along the x- and y- direction:
[tex]E_x = E cos \theta = (0.111) cos 90^{\circ}=0\\E_y = E sin \theta = (0.111) sin 90^{\circ}=0.111 m[/tex]
And
[tex]F_x = F cos \theta = (0.234) cos 300^{\circ} = 0.117 m\\F_y = F sin \theta = (0.234) sin 300^{\circ} = -0.203 m[/tex]
So the components of the vector sum are
[tex]R_x = E_x + F_x = 0+0.117 = 0.117 m\\R_y = E_y + F_y = 0.111 -0.203 = -0.092 m[/tex]
The magnitude of the vector sum is
[tex]R=\sqrt{R_x^2 +R_y^2 }=\sqrt{(0.117)^2+(-0.092)^2}=0.149 m[/tex]
And the direction is
[tex]\theta=tan^{-1} (\frac{|R_y|}{R_x})=-tan^{-1} (\frac{0.092}{0.117})=-38.2^{\circ}=321.8^{\circ}[/tex]
