If #A= <2 ,1 ,-4 ># and #B= <3 ,2 ,7 >#, what is #A*B -||A|| ||B||#?
For the dot product, we find the sum of the products for the x, y, and z terms, so we find that:
For the magnitudes, we use the distance formula for 3D vectors:
or in this case, since the vectors already give the values of
By putting all the parts together, we get: