Question

Find the cross product a × b.
a = j + 8k, b = 4i − j + 2k

Answer 1

\[
{\rm if:}\quad \vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\\
{\rm and}\quad \vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\\
{\rm then}\\
\vec{a}\times\vec{b}=\left|\begin{matrix}\hat{i}&\hat{j}&\hat{k}\\
a_1&a_2&a_3\\
b_1&b_2&b_3
\end{matrix}\right|
\]
this is the determinant.
plug in the numbers

Answer 2

\[\left[\begin{matrix}i & j & k \\ 0 & 1 & 8\\ 4 & -1 & 2 \end{matrix}\right]=i \left[\begin{matrix}1 & 8 \\ -1 & 2\end{matrix}\right]-j \left[\begin{matrix}0 & 8 \\ 4 & 2\end{matrix}\right]+k \left[\begin{matrix}0 & 1 \\ 4 & -1\end{matrix}\right]\]
\[=i[(1)(2)-(-1)(8)]-j[(0)(2)-(4)(8)]+k[(0)(-1)-(4)(1)]\]\[=10i+32j-4k\]

Answer 3

@Linyu nice work. but you have to follow the code of conduct. http://openstudy.com/code-of-conduct Cannot give away the answers just like that

Answer 4

@electrokid I understand and apologize