Question

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

Answer 1

`a`x`b=-10i-8j+3k`

Explanation:

Let vector `a=2*i-1*j+4*k` and `b=-1*i+2*j+2*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, 4),(-1, 2, 2)]`

`a`x`b=`

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

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

`a`x`b=-10i-8j+3k`

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