v-u x w-u is a vector perpendicular to the plane containing u,v,w. Divide by its magnitude to get a unit vector
uxv•w is the volume desired
check u•v u•w v•w for orthogonal
Given u=3i-2j+k,v=2i-4j-3k, w=-i+2j+2k,
1 Find a unit vector normal to the plane containing v and w.
2 Find the volume of the parallelepiped formed by u, v, and w.
3 Are any of these vectors parallel? Orthogonal? Why or why not?
1 answer
1 answer