What is the cross product of #[3, 0, 5]# and #[1,2,1] #?

1 Answer
Steve M
Dec 7, 2016

# ( (3),(0),(5) ) xx ( (1),(2),(1) ) = ( (-10),(2),(6) ) #, or #[-10,2,6]#

Explanation:

We can use the notation:
# \ \ \ \ \ ( (3),(0),(5) ) xx ( (1),(2),(1) ) = | (ul(hat(i)),ul(hat(j)),ul(hat(k))), (3,0,5),(1,2,1) |#

# :. ( (3),(0),(5) ) xx ( (1),(2),(1) ) = | (0,5),(2,1) | ul(hat(i)) - | (3,5),(1,1) | ul(hat(j)) +| (3,0),(1,2) | ul(hat(k)) #

# :. ( (3),(0),(5) ) xx ( (1),(2),(1) ) = (0-10) ul(hat(i)) - (3-5) ul(hat(j)) +(6-0) ul(hat(k)) #

# :. ( (3),(0),(5) ) xx ( (1),(2),(1) ) = -10 ul(hat(i)) +2 ul(hat(j)) +6 ul(hat(k)) #
# :. ( (3),(0),(5) ) xx ( (1),(2),(1) ) = ( (-10),(2),(6) ) #

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