Week 7 Flashcards
Normal of unit vector in R^2?
pythag
Unit vector in R^2?
u / ll u ll
Angle between vectors in R^2?
cos θ = < v , w> / ll v ll ll w ll
Cross product? between two 3x1 vectors?
det ( e1 e2 e3) sub in e1 =(1) and e2 =(0)
( a1 a2 a3) (0) (1)
( b1 b2 b3) (0) (0)
If two vectors are orthogonal?
- dot product = 0
Cross product properties?
-orthogonal to both a and b
x = p+td ? one dimensional flat
p is the particular vector from origin of r^n
x is final point
d is the direction vector with free parameter t
x = p+td +sd ? 2 dimensional flat
p is the particular vector from origin of r^n
x is final point
d is the direction vector with free parameter t and s , for x and y axis for example
Hyperplane?
(n-1) directional flat
Inconsistency in flat?
-empty flat in R^n
How can we also display a hyperplane?
<x-p , n>= 0
and each vector <d , n> = 0
Normal to a plane?
(a , b ,c)
Condition for orthogonality using directon vector and normals?
Use for SOLUTION FLATS
(n1^T) x d >= 0
(n2^T)
(n3^T)
prism?
when inconsistent
Form of a plane?
< n , (r-p) >=0
Parallel to z axis ?
(0)
(0)
(1)
How to get direction vector?
b-a , where a is the particular vector
Line interpretation?
r + td
parallel to direction vector and goes through r
If an interval is closed and continuous inside what can we infer?
- a global maxima and minima is present
