Question

What is the cross product of `[2,-1,2]` and `[4,-3,1]`?

Answer 1

the cross product
`a`x`b=+5i+6j-2k`

Explanation:

Let vector `a=2*i-1*j+2*k` and `b=4*i-3*j+1*k`

The formula for cross product

`a`x`b=[(i,j,k),(a_1,a_2,a_3),(b_1,b_2,b_3)]`

`a`x`b=+a_2b_3i+a_3b_1j+a_1b_2k-a_2b_1k-a_3b_2i-a_1b_3j`

Let us solve the cross product

`a`x`b=[(i,j,k),(2,-1,2),(4,-3,1)]`

`a`x`b=`

`+(-1)(1)i+(2)(4)j+(2)(-3)k-(-1)(4)k-(2)(-3)i-(2)(1)j`

`a`x`b=-1*i+6i+8j-2j-6k+4k`

`a`x`b=+5i+6j-2k`

God bless...I hope the explanation is useful.