How to find perpendicular vector to another vector?

How do I find a vector perpendicular to a vector like this: 3i+4j2k?
Could anyone explain this to me, please?

I have a solution to this when I have 3i+4j, 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.

Answer

There exists an infinite number of vectors in 3 dimension that are perpendicular to a fixed one.
They should only satisfy the following formula:
(3i+4j2k)v=0

For finding all of them, just choose 2 perpendicular vectors, like v1=(4i3j) and v2=(2i+3k) and any linear combination of them is also perpendicular to the original vector: v=((4a+2b)i3aj+3bk)a,bR

Attribution
Source : Link , Question Author : niko , Answer Author : Reed Richards

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