Here is a question from an assignment I am working on. The vector equation is easy.

it is X = (1,2,1) + s(-3,-1,2) + t(3,-5,3).

Everytime I try to get a linear equation out of it, I can get several equations, so I am not sure I am doing it right.

My answer works out to be 7x+15y+18z = 125

Can someone help me with this? Is my final answer correct?