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

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Answer 1 · 2016-12-10T01:16:37

$< 5, 2, 15 > \times < 4, 1, 9 > = < 3, 15, - 3 >$ $<5,2,15> xx <4,1,9> = <3,15,-3>$

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

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

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

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

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