
problem
Cross with the scalar product
Explore the meaning of the scalar and vector cross products and see how the two are related.
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?