Cross and triple vector product

A task related to cross or triple vector product in 3D-space.

Example. Vectors and are given. Find the third vector , so that { , , } form an orthogonal basis in . Normalize the vectors , , and get the orthonormal basis { , , }.

Example. Use cross product to find the sine between vectors u=(1;2;3) and v=(3;2;1).

Example. Find the volume of parallelepiped with sides u, v, w:

u = (1;4;2), v = (3;2;1), w = (-2;4;6)

Example. Use cross product to find a general equation of the plane that passes through the straight lines:

and . Here a,b,c – some constants.

Дата добавления: 2015-08-03