Question

What is the cross product of `[1, -3, 2]` and `[-8, 5, 1]`?

Answer 1

Cross product is a vector
`-13i-17j-19k`

Explanation:

Let vector `a=1*i-3*j+2*k` and `b=-8*i+5*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),(1,-3,2),(-8,5,1)]`

`a`x`b=`

`+(-3)(1)i+(2)*(-8)j+(1)(5)k-(-3)(-8)k-(2)(5)i-(1)(1)j`

`a`x`b=-3i-10i-16j-j+5k-24k`

`a`x`b=-13i-17j-19k`

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