Vector product problem

[Sonal7]

A vector perpendicular to (2i, -8j,7k), (-3i, j, -4K) is p,q, and r.

p>0 and p,q, and r are integers, with no common factors. I checked my answer 5 times but it’s incorrect. I can’t think of the alternative. I found the cross product using the determinant method and can’t see any common factors. I wonder where the error lies. It’s question 4 in the attachment.

 

[Romsek]

Oh. I see what the problem is. They want p>0. What vector maintains perpendicularity yet has p>0 ?

 

[Sonal7]

Thanks a lot. Computers aren't intelligent really

 

[Romsek]

Thanks a lot. Computers aren't intelligent really

wellll... they did ask for p>0, so the answer as entered was wrong :/

 

[Sonal7]

Oh yeah ! My intelligence!

 

[pka]

A vector perpendicular to (2i, -8j,7k), (-3i, j, -4K) is p,q, and r. p>0 and p,q, and r are integers, with no common factors. I checked my answer 5 times but it’s incorrect. I can’t think of the alternative. I found the cross product using the determinant method and can’t see any common factors. I wonder where the error lies. It’s question 4 in the attachment.

To Sonal7, There are a few facts you need to be able to quickly recall. Here are some:
the vectors \(\displaystyle \vec{v}~\&~-\vec{v}\) are both perpendicular to the same set of vectors.
Moreover \(\displaystyle \|\vec{v}\|=\|-\vec{v}\|\)

 

[Sonal7]

I guessed it ! Now I know. Thank you.