Smallest Force for a Resultant Along a Line

Force Vectors Problem Set

160 force vector problems with step-by-step solutions, from the parallelogram law to the dot product: 6 warm-ups, 10 workouts and 4 challenges on each topic.

Force Vectors: Notes, Problems and Apps

Force vectors from start to finish: nine short notes, 160 problems with step-by-step solutions and five interactive apps, from adding forces to the dot product.

Dot Product: Angle Between Vectors and Projection of a Force

Use the dot product to find the angle between two lines and the parallel and perpendicular components of a force.

Dot Product and Angle

Two Edges of a Box

Projections of a Force on Two Lines

Perpendicular or Not?

Cart on a Rail

Angle Between Two Cables from Coordinates

Cable on a Pipe

Trap Door Hinge

Space Frame Members

Cable Force Along a Beam

Wind on a Solar Panel

Cable and Pole

Projection on a Line Through Two Points

Parallel and Perpendicular Components of a Force

Angle with the Floor

Resultant from the Dot Product

Making a Right Angle