Addition of Vectors (Rectangular Components

The zero x-component makes the vector vertical. The negative y-component means downward.

(R=sqrt{9^2+12^2}=15) m.

(V_x=Vcos37^circ=10(0.8)=8) N and (V_y=Vsin37^circ=10(0.6)=6) N.

(R=sqrt{6^2+8^2}=10) N. The perpendicular components form a right triangle.

(V=sqrt{12^2+5^2}=sqrt{169}=13) m.

A vector along the negative x-axis has a negative x-component and zero y-component.

Equal and opposite vectors cancel. Therefore (R=5-5=0) N.

(F_x=Fcos60^circ=10(0.5)=5) N.

(tantheta=4/3). Hence (thetaapprox53^circ).

(V_x=Vcos90^circ=0).

(R=sqrt{12^2+5^2}=13) N.

Perpendicular components obey the Pythagorean relationship.