I have been given two points $P(0,1,3)$ & $Q(-1,5,2)$, both of them crosses a line in space. The third point is supposed to cross the line, but there is a missing coordinate $R(m,9,1)$. How do I find that missing coordinate ?
$l(x,y,z) = (0,1,3) + t(-1,4,-1)$
Thank you!
$\endgroup$ 41 Answer
$\begingroup$Your equation $(x,y,z) = (0,1,3) + t(-1,4,-1)$ can be viewed as three equations:
$$ x = 0 - t,$$
$$ y = 1 + 4t,$$
$$ z = 3 - t.$$
But you know your target:
$$ m = 0 - t,$$
$$ 9 = 1 + 4t,$$
$$ 1 = 3 - t.$$
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