70 results about "Vector projection" patented technology

The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolution of a in the direction of b) is the orthogonal projection of a onto a straight line parallel to b. It is a vector parallel to b, defined as 𝐚₁=a₁𝐛 where a₁ is a scalar, called the scalar projection of a onto b, and b̂ is the unit vector in the direction of b. In turn, the scalar projection is defined as a₁=|𝐚|cosθ=𝐚·𝐛=𝐚·𝐛/|𝐛| where the operator ⋅ denotes a dot product, ‖a‖ is the length of a, and θ is the angle between a and b.