a₁b₁+a₂b₂+a₃b₃+...+a_nb_n

||vector(a)||*||vector(b)||*cos(C)

where C is the angle formed between a and b

(a₂b₃-a₃b₂)i+(a₃b₁-a₁b₃)j+(a₁b₂-a₂b₁)k

Only defined in 3 space

||a||*||b||*sin(C)

where C is the angle between a and c

1/2 this product is the triangle formed by the two vectors

dot(a,b)/||a||

||b||cos(c)

where c is the angle formed by a and b

||cross(PQ,QR)||/||QR||

This is easy to remember because the numerator is just
twice the area of the triangle created by the

three points, the denominator is the

base.  bh/b=h

|dot(N, PQ)|/||N||

This is the just the length of the projection of the vector PQ onto the normal.

integral from a to b of: ||r`(t)||dt

where a and b are start and end value of t.

b can be substituted for t to get an arclength function.

B(t)=cross(T(t),N(t))

should have a magnitude of 1

dot(v,a)/||v||

sqrt(||a||²-a_n²)

where v is the velocity vector, a is the acceleration vector

note that this is a scalar

and

||a||²=a_t²+a_n²

||cross(v,a)||/||v||

sqrt(||a||²-a_t²)

where v is the velocity vector, a is the acceleration vector

note that this is a scalar

and

||a||²=a_t²+a_n²

||T`(t)||/||r`(t)||

||cross(v,a)||/(||v||³)

where v is the velocity vector, a is the acceleration vector

note that this is a scalar

Vector Valued
Symmetric
and Parametrized Forms

of line from <a,b,c> to <d,e,f>

r(t)=((d-a)t+a)i+((e-b)+b)j+((f-c)+c)k

(x-a)/(d-a)=(y-b)/(e-b)=(z-c)/(f-c)

x=(d-a)t+a; y=(e-b)t+b; z=(f-c)t+c