How do I find a vector perpendicular to a vector like this: 3i+4j−2k?

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+4j−2k)⋅v=0

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

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