determine the relative position of line (d):$( x=2t+3; y=-t+1; z=3t+2)$ and plane (P):$2x-y-z+2=0$ and determine the coordinates of the intersection point if it exists.
2026-03-25 12:33:50.1774442030
relative position of a line and a plane
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Hint:
substitute the $x,y,z$ of the line in the equation of the plane and solve for $t$. If you have one solution $t=t_0$ , using this value in the equation of the line you find the common point.