What is the cross product of #[2, -1, 4]# and #[5, 2, -2] #?

1 Answer
Steve M
Feb 25, 2017

# <2,-1,4> xx <5,2,-2> = <-6,24,9> #

Explanation:

We can use the notation:

# \ \ \ \ \ ( (2),(-1),(4) ) xx ( (5),(2),(-2) ) = | (ul(hat(i)),ul(hat(j)),ul(hat(k))), (2,-1,4),(5,2,-2) |#

# " " = | (-1,4),(2,-2) | ul(hat(i)) - | (2,4),(5,-2) | ul(hat(j)) +| (2,-1),(5,2) | ul(hat(k)) #

# " " = (2-8) ul(hat(i)) - (-4-20) ul(hat(j)) +(4+5) ul(hat(k)) #

# " " = -6 ul(hat(i)) +24 ul(hat(j)) +9 ul(hat(k)) #
# " " = ( (-6),(24),(9) ) #

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