MATH 20C Lecture 4

Intersection of Two Lines

Remark: We say and intersect if for some .
and collide if for some t.

Surfaces in

Sphere

R: radius, center

Cylinder

radius R, central axis
Cylinder of radius R whose central axis is the vertical line through is

Dot Product

$\Vert \vec{v}\Vert =\sqrt{\vec{v}\cdot \vec{v}}$

Properties of the Dot Product

4. 
   

$\vec{v}\cdot \vec{w}=\Vert \vec{v}\Vert \Vert \vec{w}\Vert \cos \theta ,0\le \theta \le \pi$

If

Angle between two vectors

1. (Orthogonal/Perpendicular)
2. is obtuse
3. is acute

Projections

Assume

1. The projection of along is
   
2. The scalar is called the component or scalar component of along
3. is orthogonal to
4. where is parallel to and is perpendicular to