How carry out I find the points in ~ which the line given by the symmetric equation:$$\\frac-x - 1-1 = \\fracy + 52 = \\fracz - 6-3$$intersects the coordinate planes $xz$, $yz$, $xy$?


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One idea:First create the line as parametric equations:$$\\beginalignx &= -1 +t \\\\y &= -5 + 2t \\\\z &= 6 - 3t.\\endalign$$You have intersection through $xy$-plane as soon as $z=0$, so that provides $t=2$ which gives you the suggest of intersection $(1, -1, 0)$. Now do an in similar way for the various other planes.

You are watching: Find the points in which the required line in part (a) intersects the coordinate planes.


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Hint: simply do it. Because that example, the intersection with the coordinate plane $xz$ way that $y=0$, which offers

$$ \\frac -x-1-1 = \\frac 0 + 52 = \\frac z-6-3. $$


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