Question

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

Answer 1

`( (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) )`