1
$\begingroup$

If I understand correctly, the cross product of vectors $a$ and $b$ is orthogonal to both $a$ and $b$.

So for an assignment I have to find two unit vectors orthogonal to vector $a = \langle 1,0,4 \rangle$ and $b = \langle 1,-4,2 \rangle$.

The cross product of those two vectors is according to my calculation $\langle 16,2,-4 \rangle$.

Now I have to calculate the unit vector of the cross product, which is according to my calculation $\displaystyle \frac{1}{\sqrt{264}} \langle 16,2,-4 \rangle$, but apparently this is incorrect as the answer must be, according to mybook, $\displaystyle \frac{1}{\sqrt{69}} \langle 8,1,-2 \rangle$ or the same thing but negative?

|cite|improve this question
$\endgroup$
  • $\begingroup$ 256 + 4 + 16 = 276 $\endgroup$ – Will Jagy Sep 20 '14 at 22:03
  • 1
    $\begingroup$ In addition to Rory's answer, notice $(16,2,-4)$ and $(8,1,-2)$ differ only by a factor $2$. $\endgroup$ – Stop hurting Monica Sep 20 '14 at 22:40
1
$\begingroup$

You made a calculation error while finding the length of the vector <16,2,-4>. The length is $\sqrt {276}$, not $\sqrt {264}$. If you correct that, you will find that your answer, after simplification, is the same as the book's. (I have corrected an error pointed out by user84413 and added detail suggested by Jean-Claude Arbaut: thanks to both.)

|cite|improve this answer
$\endgroup$
  • 2
    $\begingroup$ (I think you mean the square of the length is 276.) $\endgroup$ – user84413 Sep 20 '14 at 22:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.