Calculus

Cross Product

1. Compute the cross product ~a ·~b if ~a = 6̂i − 10ĵ + 10k̂ and ~b = −7̂i − 4ĵ − 3k̂.

2. Find < 0, 3, 7 > × < 2, −3, 7 >.

3. If ~v × ~w =< 7, −7, −1 > what is the value of (−2~v − 2~w) × ~w?

4. Find the area of the parallelogram with vertices P(0, 0, 0), Q(1, −2, 2), R(1, −1, 1), S(2, −3, 3).

5. Find a vector perpendicular to both < 6, 4, 5 > and < 8, 3, 1 >.