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

Question

1867 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-07T01:22:12

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

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

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

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

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

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