1. ## Perpendicular Vectors

Hi again

I am looking for a unit vector that is perpendicular to the following vectors

$\displaystyle a= 3i-j+4k$
$\displaystyle b=-3i-2j+2k$

So I know that find a perpendicular vector that $\displaystyle a.b=0$

So I get $\displaystyle (3,-1,4).(-3,-2,2)= (-9,2,8)$ but this isn't one of the options. I know that multiples of it can be also perpendicular, can someone point out where I'm going wrong?

Thanks

2. OK... I have seen an error in what I'm doing here. I want a vector perpendicular to both of them - they aren't perpendicular to each other so I can't find the dot product of a and b.

So what would I do instead? I'm very confused

3. Hello,
Originally Posted by Ian1779
OK... I have seen an error in what I'm doing here. I want a vector perpendicular to both of them - they aren't perpendicular to each other so I can't find the dot product of a and b.

So what would I do instead? I'm very confused
Do you know about the cross product ? (Cross product - Wikipedia, the free encyclopedia)

There's the formula in this section The explanation of what the cross product is is above.

And if you want a unit vector, once you get the result of the cross product, divide each ordinate by the length of the vector, that is $\displaystyle \sqrt{x^2+y^2+z^2}$ for a vector (x,y,z)

4. I did know about the cross product, but didn't realise I had to use it in this context.

I've now got the cross product which is $\displaystyle 6i+18j-9k$

So I am dividing this now by $\displaystyle \sqrt{6^2+18^2+(-9)^2}$ Is that right? If so I think I'm there giving me

$\displaystyle {\frac{2}{7}}i+{\frac{6}{7}}j-{\frac{3}{7}}k$

I hope I've got it?!

5. You missed a sign in the cross product: $\displaystyle 6i-18j-9k$

6. Originally Posted by Ian1779
I did know about the cross product, but didn't realise I had to use it in this context.

I've now got the cross product which is $\displaystyle 6i-18j-9k$

So I am dividing this now by $\displaystyle \sqrt{6^2+18^2+(-9)^2}$ Is that right? If so I think I'm there giving me

$\displaystyle {\frac{2}{7}}i-{\frac{6}{7}}j-{\frac{3}{7}}k$

I hope I've got it?!
You can check by doing the scalar product with each of the other vectors =)
You can also check whether or not it is a unit vector, by calculating the norm of the latter vector.