Question

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

Answer 1

`color(blue)(a " x " color(blue)(b=-6i-11j+8k)`

Explanation:

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

`a`x`b=`

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

`a`x`b=+4*i-10i-5j-6j+6k+2k`

`a`x`b=-6i-11j+8k`

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