I have the vecotr:
$$\vec v = (-3,4,-5)$$
And the plane: $$\pi:\\x=1-\lambda\\y=-2\\z=\lambda -\mu$$
I need to decompose the vector $\vec v$ as the sum of a vector perpendicular to the plane and the other vector parallel to it. I tried projecting $\vec v$ into a vector of the plane and also projecting it into the normal of the plane, but this is not the answer. I think that even if I Project the $\vec v$ into these two vectors, I still need a third componente such that the sum of these $3$ vectors will be $\vec v$.
What am I doing wrong?