How do I find the points at which the line given by the symmetric equation: $$ \frac{-x - 1}{-1} = \frac{y + 5}{2} = \frac{z - 6}{-3} $$ intersects the coordinate planes $xz$, $yz$, $xy$?
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One idea: First write the line as parametric equations: $$ \begin{align} x &= -1 +t \\ y &= -5 + 2t \\ z &= 6 - 3t. \end{align} $$ You have intersection with $xy$-plane when $z=0$, so that gives $t=2$ which gives you the point of intersection $(1, -1, 0)$. Now do likewise for the other planes. |
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Hint: Just do it. For example, the intersection with the coordinate plane $xz$ means that $y=0$, which gives $$ \frac {-x-1}{-1} = \frac {0 + 5}{2} = \frac {z-6}{-3}. $$ |
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