Scalar Notation

Consider a man pulling a rope from a hook in the northeast direction.

Force vector is denoted as F₁. It is resolved into scalar components, represented as F_1x along the x-axis and F_1y along the y-axis.

The direction, which is the angle made by F₁ with the positive x-axis in the anticlockwise direction, is the tan inverse of the y component over the x component.

Here, F_1x and F_1y are rectangular components forming a right triangle and can be obtained using trigonometric functions.

If another force F₂ acts on the hook from the southeast direction, then F_2x is along the positive x-axis, and F_2y is along the negative y-axis.

The x and y components of F₂ are obtained using the trigonometric function, and the resultant force is the algebraic sum of the components of both the forces along the x and y axes, whereas its magnitude is obtained by using the square root of the sum of the squares of its components.