HELP! Find v × w if v = 3i + 8j – 6k and w = –4i – 2j – 3k.A. –2i + 8j – 3kB. –36i + 33j + 26kC. 33i + 26j + 8kD. 3i – 2j + 8k

Using the determinant method, the cross product is[tex]\begin{vmatrix}\vec\imath&\vec\jmath&\vec k\\3&8&-6\\-4&-2&-3\end{vmatrix}=\begin{vmatrix}8&-6\\-2&-3end{vmatrix}\,\vec\imath-\begin{vmatrix}3&-6\\-4&-3\end{vmatrix}\,\vec\jmath+\begin{vmatrix}3&8\\-4&-2\end{vmatrix}\,\vec k=-36\,\vec\imath+33\,\vec\jmath+26\,\vec k[/tex]so the answer is B.Or you can apply the properties of the cross product. By distributivity, we have(3i + 8j - 6k) x (-4i - 2j - 3k)= -12(i x i) - 32(j x i) + 24(k x i) - 6(i x j) - 16(j x j) + 12(k x j) - 9(i x k) - 24(j x k) + 18(k x k)Now recall that(i x i) = (j x j) = (k x k) = 0 (the zero vector)(i x j) = k(j x k) = i(k x i) = j(a x b) = -(b x a) for any two vectors a and bPutting these rules together, we get(3i + 8j - 6k) x (-4i - 2j - 3k)= -32(-k) + 24j - 6k + 12(-i) - 9(-j) - 24i= (-12 - 24)i + (24 + 9)j + (32 - 6)k= -36i + 33j + 26k