Vectors and Lines

Question	Answer
length of vector	sqrt(x^2+y^2+z^2)
If v and w are non-zero vectors in R3 when does	if and only if v and w have the same length and direction
Geometric Vectors	the line segment from a point to another, the length and direction are what is important not the location.
The Parallelogram Law	In the parallelogram determined by two vectors v and w, the vector v+w is the diagonal with the same tail a v and w.
Scalar Multiplication Law	If a is a real number and v is a non-zero vector then the length if av is \|a\|\|\|v\|\| and the direction is opposite iff a<0
The vector equation of a line	p=p0+td where t is any scalar ie. the point p is on this line if a real number t exists st p=p0+td
Parametric Equation of a Line	The line through P0(x0,y0,z0) with direction vector d=(a,b,c)≠0 is given by x=xo+ta y=yo+tb z=zo+tc t is any scalar
v•v=?	\|\|V\|\|^2
v•w=	w•v
(kv)•w	k(w•v) fora all scalars k
u•(v±w)	u•v±u•w
\|\|v\|\| \|\|w\|\| cos◊	v•w
two vectors are orthogonal if	v•w=0 or the angle btw them is π/2
The projection of u on d	projd u = u•d/\|\|d\|\|^2 d
the vector u - projd u is...	orthogonal to d

Resource summary

	Created by Kaitlin McNeil over 8 years ago