Find the intersection points of the line L with the three coordinate planes Oxy, Oyz, and Ozx

Question

Let L be the line given by the parametric equations x = 1 + 2t, y = −1 − t, z = 3t Find the intersection points of the line L with the three coordinate planes Oxy, Oyz, and Ozx

Answer 1

Hint: For example, for the $x$-$z$ plane, you want $y=0$, so $-1-t=0$, meaning that $t=-1$. Substitute. We get $(-1,0,-3)$.