What is the cross product of #<5, 2 ,15 ># and #<4 ,1 ,9 >#?

1 Answer
Steve M
Dec 10, 2016

# <5,2,15> xx <4,1,9> = <3,15,-3> #

Explanation:

We can use the notation:
# \ \ \ \ \ ( (5),(2),(15) ) xx ( (4),(1),(9) ) = | (ul(hat(i)),ul(hat(j)),ul(hat(k))), (5,2,15),(4,1,9) |#

# :. ( (5),(2),(15) ) xx ( (4),(1),(9) ) = | (2,15),(1,9) | ul(hat(i)) - | (5,15),(4,9) | ul(hat(j)) +| (5,2),(4,1) | ul(hat(k)) #

# :. ( (5),(2),(15) ) xx ( (4),(1),(9) ) = (18-15) ul(hat(i)) - (45-60) ul(hat(j)) +(5-8) ul(hat(k)) #

# :. ( (5),(2),(15) ) xx ( (4),(1),(9) ) = 3 ul(hat(i)) +15 ul(hat(j)) -3 ul(hat(k)) #
# :. ( (5),(2),(15) ) xx ( (4),(1),(9) ) = ( (3),(15),(-3) ) #

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