I have three non-parallel vectors (whose components are known), v0, v1, v2 and I'd like to find a fourth unit vector, v3, given only the angles between:(adsbygoogle = window.adsbygoogle || []).push({});

psi, angle between v0 and v3

theta, angle between v1 and v3

phi, angle between v2 and v3

I know that they are related by the dot product:

v0 . v3 = |v0||v3| cos(psi)

v1 . v3 = |v1||v3| cos(theta)

v2 . v3 = |v2||v3| cos(phi)

this give me a system of equations to solve,

however, I have a term on the right side |v3|, expands into sqrt(a^2+b^2+c^2) - so its not quite linear.

If I have the constraint that I want to find a UNIT vector v3, ie. |v3|=1, then can i just set sqrt(a^2+b^2+c^2)=1, to make it a linear system?

Also - is there an easier way to solve this?

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# Finding the a vector using angles

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