Chapter 1 – Scalar and Vector Products

Key vocabulary for understanding scalar (dot) and vector (cross) products, their formulas, and their role in determining a resultant force.

Scalar Product

Also called the dot product; an operation that multiplies two vectors to produce a scalar quantity.

Dot Product Formula

A · B = |A| |B| cos θ, where θ is the angle between vectors A and B.

Vector Product

Also called the cross product; an operation that combines two vectors to produce a third vector perpendicular to the originals.

Cross Product Magnitude

|A × B| = |A| |B| sin θ, giving the size of the resulting vector.

Right-Hand Rule

A method for finding the direction of A × B: point your fingers along A, curl toward B, and your thumb points in the product’s direction.

Resultant Force

The single force obtained by vector addition (via dot or cross products as needed) that has the same effect as all individual forces combined.