Scalars and Vectors in Statics

Resultant of Two Forces 60° Apart

Hook on a Wall

Pulling a Sled

Adding Forces: Parallelogram Law and Triangle Rule

Find the resultant of two or more forces with the parallelogram law, the triangle rule and the laws of sines and cosines.

Resultant of Two Perpendicular Forces

Difference of Two Forces

Resolving a Force into Components Along Two Axes

Split a force into components along any two given directions, and see why oblique components are not projections.

Pulling Down a Tree

Two Tugboats on a Ship

Two Tractors on a Stuck Truck

Rectangular Components of a Force in 2D

Write a force by its x and y components, in scalar and Cartesian vector form, and get its magnitude and direction back.

Moving a Pallet Down an Aisle

Cable Angle for a Required Resultant

Resultant of Coplanar Forces by Rectangular Components

Add any number of coplanar forces by summing x and y components, and find an unknown force from a known resultant.

The Missing Force on a Bracket

Three Ropes, Two Triangles

How Big Can the Resultant Be?

Cartesian Vectors in 3D: Components and Direction Angles

Describe a force in 3D with i, j, k components, its magnitude, coordinate direction angles and unit vector.

Pulling a Car Out of a Ditch

Second Force for a Vertical Resultant on a Hook