4.5.1—Scalar product

a·b=a₁b₁+a₂b₂=|a||b|cosθ. It is zero for perpendicular vectors and gives the component of one vector along another after division by the reference magnitude.

Check both vectors are non-zero, use the principal angle and preserve units when a physical projection is requested.

For a=(2,1) and b=(1,2), a·b=4 and cosθ=4/5.

The dot product is not |a||b| without the cosine factor and is not a vector direction.