How to find perpendicular vector to another vector? How do I find a vector perpendicular to a vector like this: $$3\mathbf{i}+4\mathbf{j}-2\mathbf{k}?$$
Could anyone explain this to me, please?
I have a solution to this when I have $3\mathbf{i}+4\mathbf{j}$, but could not solve if I have $3$ components...
When I googled, I saw the direct solution but did not find a process or method to follow. Kindly let me know the way to do it. Thanks.

Remember:  There exist infinite vector in 3 dimension that are perpendicular to a fixed one. 
Now, 
Let $v\neq 0$ be the vector  whose is $xi+yj+zk$.
 So , $v$ is perpendicular to the vector $3i+4j-2k$.
Therefore,   $v\cdot\langle 3i+4j−2k\rangle=0$.
$$
                      \langle xi+yj+zk\rangle\cdot \langle3i+4j−2k\rangle =0
$$ 
so $3x+4y-2z=0$ (1)   where $i\cdot i =j\cdot j=k\cdot k=1$.
Now, there are three unknown variable such x, y and z  in (1).
 You can choose any two variable whatever you like.
Let $y=2$ and $z=1$,
then $x=-2$     from (1),
One of the vector is $(-2i+2j+k)$.
 Similarly,  you can choose  one of two variables  from (1) , then find the third variable. 
So, you can find infinite perpendicular vectors to  the vector $3i+4j-2k$.
