MATH 20C Lecture 5

Projection: Given $\vec{v}\ne \vec{0}$

is the projection of onto .
is the component of perpendicular to .

${\vec{u}}_{\Vert \vec{v}}$

Where

Find the distance from the point $P=(5,1,-3)$ to the line $L=⟨x(t),y(t),z(t)⟩=⟨4,4,2⟩t$

Choose

distance


distance =

12.4 Cross Product

Determinant $\in \mathbb{R}$

Cross Product of 3D Vector

Geometric Facts of Cross Product

1. is orthogonal to and
2. The direction of is determined by the right-hand rule

Basic Properties of the Cross Product

3. for some
5.