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

1. 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

2. 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
Let the sought vector be $\textbf u=a\,\textbf i+b\,\textbf j+c\,\textbf k\text.$ The two vectors must be orthogonal, so

$4a-3b+c=0$

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

$c=0\text.$

Substituting, that means $4a-3b=0\Rightarrow a=\frac34b\text.$ Choose an arbitrary pair of numbers that satisfy the equation to get a vector $c\textbf u$, and then find the unit vector in the same direction.

3. Thanks Reckoner your the best and I could understand it!
I have another question hope you'll be able to answer it too!