# Gr 12. Vector Question Involving Dot Product of Two Vectors(Part 2)

• Feb 17th 2009, 02:46 PM
narutoblaze
Gr 12. Vector Question Involving Dot Product of Two Vectors(Part 2)
I don't know if I'm being abusive posting another thread so let me know if there is a limit on how much question/threads I can post a day in this forum or any other thanks! But I got another tricky question, much more trickier!

Find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k (4, -3, 1)

So how would I go about doing this questions? Thanks:D
• Feb 17th 2009, 03:12 PM
Reckoner
Quote:

Originally Posted by narutoblaze
I don't know if I'm being abusive posting another thread so let me know if there is a limit on how much question/threads I can post a day in this forum or any other thanks! But I got another tricky question, much more trickier!

Find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k (4, -3, 1)

So how would I go about doing this questions? Thanks:D

Let the sought vector be $\displaystyle \textbf u=a\,\textbf i+b\,\textbf j+c\,\textbf k\text.$ The two vectors must be orthogonal, so

$\displaystyle 4a-3b+c=0$

But $\displaystyle \textbf u$ is parallel to the $\displaystyle xy$-plane, so we must also have

$\displaystyle c=0\text.$

Substituting, that means $\displaystyle 4a-3b=0\Rightarrow a=\frac34b\text.$ Choose an arbitrary pair of numbers that satisfy the equation to get a vector $\displaystyle c\textbf u$, and then find the unit vector in the same direction.
• Feb 17th 2009, 03:27 PM
narutoblaze
Thanks Reckoner your the best and I could understand it!(Bow)
I have another question hope you'll be able to answer it too!