Vector Algebra

A scalar has magnitude only

A scalar has magnitude only, while a vector has both magnitude and direction. A directed line segment represents a vector. Common scalar quantities in

The vector from the origin O

The vector from the origin O to a point P(x,y,z) is the position vector of P. Its magnitude is |OP| = √(x² + y² + z²). In component form, it is writte

If a vector makes angles α

If a vector makes angles α, β, γ with the positive x-, y-, and z-axes, then cos α, cos β, cos γ are its direction cosines l, m, n. They satisfy l² + m

A zero vector has coincident initial

A zero vector has coincident initial and terminal points and is denoted by 0⃗. It has zero magnitude and no definite direction. A unit vector has magn

The triangle law gives AC⃗ =

The triangle law gives AC⃗ = AB⃗ + BC⃗. The parallelogram law says that the diagonal through the common point represents the sum of two coinitial vect