Vectors

Formulae/methods for first year university vectors. No matrices.

dot product calculation

in \mathbb{R}²,

(a₁b₁ + a₂b₂)

cross product calculation in \mathbb{R}^3

Calculate determinant of the matrix, for x,y,z.

What property does the cross product have?

The cross product is orthogonal to both/all vectors that are crossed.

i.e. a x b is orthogonal to a and b

What does it mean for vectors to be orthogonal? What about a vector orthogonal to a plane?

Vectors are perpendicular to each other.

Vector is perpendicular to the plane.

Formula for area of a triangle?

A=\frac12||a\times b||

What is the scalar triple product (formula)?

u\cdot\left(v\times w\right)

How do I calculate the volume of a parallelepiped

Magnitude of triple scalar product

\left|u\cdot\left(v\times w\right)\left|\right.\right.

What is a parallelepiped?