Expert: David Hemmer - 4/18/2007

Question
Hi i have been stuck on this question all holidays and have given up. Any chance you could show me how its done?
Any help appreciated.
Cheers
Scott

1.Let u=2i-3j+4k, v=i-j+2k. Find(using the cross product):
a)a vector perpendicular to both u and v
b)the area of the parallelogram defined by u and v
C)the sine of the angle between u and v

Answer
u=(2,-3,4) v=(1,-1,2)

a. The cross product is perpendicular to both. In this case it is (-2, 0, 1)

b. The area of the par. is the length of the cross product which is sqrt(4+0+1) =sqrt(5).

c. I'll just give you a hint on this one. |uxv|=|u||v|sintheta

where theta is the angle between the vectors.

As an aside this would be an elementary problem I'd give in calc III so if you are taking calc 3 you need some help! If you are in physics then that's another story.