466506…: “On the windless square”

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Which of the following represents a line that passes through the point $(2,0,3)$ and is orthogonal to the plane $x-y+3z=12$ ?

$\vec {r}(t) = \vector {2t+1,-1,3t+3}$ $\vec {r}(t) = \vector {t+2,-t,3t+3}$ $\vec {r}(t) = \vector {t,-t+4,3t2}$ $x-y+3z = 11$ $2x+3z=11$ $2x-y-z=1$ There is no such line. None of the above

Which of the following represents a plane that passes through the point $(2,0,3)$ and is orthogonal to the plane $x-y+3z=12$ ?

$\vec {r}(t) = \vector {2t+1,-1,3t+3}$ $\vec {r}(t) = \vector {t+2,-t,3t+3}$ $\vec {r}(t) = \vector {t,-t+4,3t2}$ $x-y+3z = 11$ $2x+3z=11$ $2x-y-z=1$ There is no such line. None of the above