Perpendicular vector question

[Guest]

Hi
Can you check my answer to this qusetion as the given answer is different and I would like to know where I've gone wrong?

Find a vector which is perpendicular to \(\displaystyle A\vec B\left( \begin{array}{r}
- 2 \\
1 \\
- 4 \\
\end{array} \right){\rm and }C\vec D\left( \begin{array}{r}
1 \\
2 \\
- 1 \\
\end{array} \right)\).

I tried to work out the vector product in order to find the normal, n, to these lines:


\(\displaystyle {\rm let }n = \left| {\begin{array}
i & j & k \\
{ - 2} & 1 & 4 \\
1 & 2 & { - 1} \\
\end{array}} \right| = {\bf i}( - 1 - 8) - {\bf j}(2 - 4) + {\bf k}( - 4 - 1)\)

$\displaystyle = - 9{\bf i} + 2{\bf j} - 5{\bf k}$


The anwer given in class was $\displaystyle 7{\bf i} - 6{\bf j} - 5{\bf k}$

but I just dont seem to be able to get the same result.
Please help.

 

[skeeter]

note that vector AB is <-2, 1, -4>

you used +4 in your calculation