Vectors Formulas Flashcards
What is the formula of D for r x n = D (scalar eqn) of a plane
n * point on plane (a)
what is the angle formula for a dot b
|a| |b| cos@
what is a dot a
a |^2
How to prove two vectors are perpendicular?
a dot b = 0
What is the angle formula for a x b
(|a||b|sin@) * unit vector
What is a x a (vectors)
a x a = 0
How to prove two vectors are parallel
a x b = 0
How to find area between 2 vectors
Parallelogram: | a x b |
Triangle : half of ^^
Formula for vector of projection v
(a • b (hat)) * b(hat)
Formula for magnitude of projection vector
a • b(hat)|
Formula for vector of vector component
a - (a•bhat) *bhat
Formula for magnitude of vector component
a - (a•bhat) *bhat|
What is the vector equation of line
L: r = a + &m, &=real
What is the parametric equation of a line
x = a1 + &m1
y = a2 + &m2
x = a3 + &m3
What is the Cartesian equation of a line
L: (x - a)/m
Make & the subject for each parametric eqn
What is the vector eqn of a plane
p: r = a + &m1 + $m2, &$ = real
What is the scalar equation of a plane
r • n = D
D = n • a
What is the Cartesian eqn of a plane
P: ax + by + cz = D
