Question

Adding Two Dot Products

How does r'(t)·r(t) + r(t)·r'(t) = 2r'(t)·r(t) ?

Answer 1

the dot product commutes.

let A= (a,b)
and B= (x,y)
A dot B = a*x + b*y
B dot A = x*a + y*b
but x*a = a*x and y*b= b*y B dot A matches A dot B

Answer 2

that means A \( \cdot \) B + B ⋅ A = A ⋅ B + A ⋅ B = 2 A ⋅ B