Let w be a vector in R3. Show that ||w, u x v || = ||w||(||u||)||v||sin(theta)(sin(psi)) where psi is the angle between the vector w and the plane determined by the vectors u and v.
Let w be a vector in R3. Show that ||w, u x v || = ||w||(||u||)||v||sin(theta)(sin(psi)) where psi is the angle between the vector w and the plane determined by the vectors u and v.
Where is the angle between and , and is the normal to the plane defined by and , and is the angle between the normal and , and so is the angle between the plane and .