Answer
Pythagorean Theorem is verified.
Work Step by Step
Given the vectors ${u}=(3,4,-2), \quad {v}=(4,-3,0)$, then their lengths can be calculated as follows
$$\|{u}\|^2=9+16+4=29, \quad \|{v}\|^2=16+9+0=25.$$
Since $u+v=(7,1,-2)$, then
$$\|{u+v}\|^2=49+1+4=54.$$
One can see that,
$$\|{u}+{v}\|^{2}=\|{u}\|^{2}+\|{v}\|^{2}$$
Hence, Pythagorean Theorem is verified.