Glossary - V
All terms beginning with the letter 'T' are shown below:
| Vector: | ??? |
| Vector cross product: | c = a × b is a vector that is perpendicular to the plane spanned by vectors a and b. The direction that c points in is determined by the right hand rule. Note a × b = −b × a. The cross product is most easily calculated as the determinant of the matrix \[ {\bf a} \times {\bf b} = \begin{vmatrix} {\bf i} & {\bf j} & {\bf k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{vmatrix} . \] |
| Vector dot product: | \[ {\bf u} \bullet {\bf v} = u_1 v_1 + u_2 _2 + \cdots + u_n v_n . \] In three dimensional case, \[ {\bf u} \bullet {\bf v} = \| {\bf u} \| \cdot \| {\bf v} \| \cdot \cos\theta , \] where θ is angle between vectors, and ∥v∥ is the Euclidean length of vector v. |
| Vector fields: | A vector field F(x,y,z,t) returns a vector for every point in space and is readily visualized as a field of arrows. Examples include velocity, elastic displacements, electric or magnetic fields. |
| Vector triple product: | ??? |
| Vector wedge product: | ??? |