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**o_O** Let this point be $\displaystyle C(a,b,c)$ and $\displaystyle \vec{OC} = (a,b,c)$

Since C is on the line, we can see that: $\displaystyle a = 1 + 3\lambda, b = 7 - \lambda, c = -5 + 2\lambda$

Since $\displaystyle \vec{OC} \perp (3, -1, 2) $, then $\displaystyle \vec{OC} \cdot (-3,-1,2) = 0$:

$\displaystyle -3a - b + 2c = 0$

Convert a,b, c into terms of lambda and solve for it. Then, plug it in back to the equation of your line to get $\displaystyle \vec{r}$ which should correspond to your point as it originates form the origin.