What is the magnitude of a vector a = (a1, a2, a3)?
|a| = √(a1² + a2² + a3²)
What is the unit vector in the direction of a?
â = a / |a|
What is scalar multiplication of a vector?
λa = (λa1)i + (λa2)j + (λa3)k
What is vector addition?
a + b = (a1 + b1)i + (a2 + b2)j + (a3 + b3)k
What is the scalar (dot) product?
a · b = |a||b| cos θ
If a ⟂ b → a · b = 0
cos θ = (a · b) / (|a||b|)
What is the vector (cross) product?
a × b = (a2b3 − a3b2)i + (a3b1 − a1b3)j + (a1b2 − a2b1)k
What is the triple scalar product?
(a × b) · c = a · (b × c) = b · (c × a)
What is the triple vector product?
a × (b × c) = (a · c)b − (a · b)c
How do you represent a line through points A and B?
r = a + s(b − a) If r = xi + yj + zk → x = a1 + s(b1 − a1) y = a2 + s(b2 − a2) z = a3 + s(b3 − a3)
What is the equation of a plane?
Given point (x0, y0, z0) and normal n = (n1, n2, n3): (x − x0)n1 + (y − y0)n2 + (z − z0)n3 = 0 or equivalently: n1x + n2y + n3z = d, where d = n1x0 + n2y0 + n3z0
