Find two perpendicular vectors from another vector
I have a vector1 that I know 3D coordinates (vector1 can be in any direction) and I would like to find two perpendicular vectors to this vector 1 (the two perpendicular vectors must be perpendicular to each other).
What's the fastest way to find two vectors programmatically (in Java if possible)?
I tried to rotate vector1 90 degrees, but it doesn't seem to always work depending on the direction of the vector.
Edit: Perpendicular vectors can be in any direction.
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To find the first vector, you can apply the following algorithm:
Suppose the original vector (A, B, C)
. Two vectors are perpendicular if their dot product is 0. So, we get the equation A * x + B * y + C * z = 0
. At least one of A
, B
or C
not equal to zero. Let's assume it is C
not zero. Then the vector ( 1
, 1
, -(A + B) / C
) is suitable. A case where C = 0
, but A != 0
or B != 0
can be handled in a similar way.
Finding the second vector is much easier: you can use the cross product of the original vector and the first vector. What is it.
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