Distance between two 3D points
Equation of a sphere
Vector subtraction
Example C shows the most useful way of picturing vector subtraction.
Magnitude of a 3D vector
Normalizing a vector
u represents a resultant unit vector.
Normalizing a vector results in a unit vector.
Dot product of two vectors
Properties of the dot product
Dot product of two vectors (physics definition)
Angle between two nonzero vectors
Scalar projection of vector b onto vector a
Vector projection of vector b onto vector a
Orthogonal projection of vector b onto line spanned by a
Cross product of two vectors
The vector a x b is orthogonal to both a and b.
Magnitude of cross product
Cross product of parallel vectors
The result is the zero vector, not the scalar.
Properties of the cross product
Volume of the parallelepiped
Specifically, a parallelepiped determined by vectors a, b, and c.
Scalar triple product
Distributing a scalar over a cross product
Vector triple product
Scalar equation of a plane
Distance from a point to a plane
