Let $U$ be the line intersection of the planes $x + y + z = 0$ and $4x + y + z = 0$. Let $T:\mathbb{R}^3\rightarrow U$ be the projection of $\mathbb{R}^3$ onto U. Find the formula for $T(x, y, z)$
This is a problem in my textbook. Finding the equation of the line is easy: The equation of line is: $[0 -1 1] * t$
But second part, finding the formula, I don't understand so much. And I cannot find connection in the phrase "onto U" to solve this problem.
Thanks :)