C Roettger, Fall 14
Math 265 Quiz 2C – Solutions
Problem 1 Consider the vectors u = (3, 2, −4) and v = (1, 2, 0).
a) Find the cross product u × v.
b) Find the area of the triangle with vertices (0, 0, 0, (3, 2, −4), and (1, 2, 0).
Solution. a) Any way you like to compute this is fine.
u × v = (0 + 8)i − (0 + 4)j + (6 − 2)k = (8, −4, 4).
This triangle has two sides (the two meeting in the origin) given by u and v
(coincidence?!?!?). Its area is half the area of the parallelogram determined
by u and v, so
√
√
64 + 16 + 16 √
1
= 24 = 2 6.
A = ||u × v|| =
2
2