The Gram-Schmidt process applies a series of projections to these objects. A certain operation on three of these gives the volume of a parallelepiped. One operation on these objects is anti-commutative, and two of these are orthogonal if another operation yields zero; those 
The Gram-Schmidt process applies a series of projections to these objects. A certain operation on three of these gives the volume of a parallelepiped. One operation on these objects is anti-commutative, and two of these are orthogonal if another operation yields zero; those operations are the cross and dot products. Sometimes written as a one-column matrix, the sum of two of these can be represented as the diagonal of a parallelogram. Contrasted with scalars, for 10 points, name these mathematical objects that have both magnitude and direction.
The Gram-Schmidt process applies a series of projections to these objects.
{vectors} [accept {vector quantities}, do not accept "{vector fields}"]