Vectors Revision Flashcards
1
Q
Rotation matrices
A
are unitary
U^(+) = U^(-1)
=> UU^(=) = II
2
Q
scalar dot product
A
|a||b|cosθ
3
Q
cross product
A
a x b = c
|c|=|a||b|sinθ
4
Q
projection of a onto b:
A
a(hat) . b
5
Q
Parametric forms
A
r -> r(t)
6
Q
how to find the normal to plane
A
r . (coefficients) + 1 = 0
compare to r . n(hat) = d
7
Q
shortest distance to a plane
A
identify a point on the plane (setting two coords to zero)
project p - r onto n.
8
Q
shortest distance between two lines
A
n = a x b
n = a x b / |a x b|
9
Q
scalar triple product is equivalent to
A
the volume of a parallelpiped
