# The points (2, -1, -2), (1, 3, 12), and (4,

letumsnemesislh 2022-07-02 Answered
The points (2, -1, -2), (1, 3, 12), and (4, 2, 3) lie on a unique plane. Where does this plane cross the z-axis?
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## Answers (1)

lydalaszq
Answered 2022-07-03 Author has 11 answers
Step 1
By Gaussian elimination,
$\left\{\begin{array}{l}2a-b-2c=d,\\ a+3b+12c=d,\\ 4a+2b+3c=d\end{array}$
$\left\{\begin{array}{l}\frac{7}{2}b+13c=\frac{d}{2},\\ 4b+7c=-d\end{array}$
$-\frac{55}{2}c=-\frac{11}{2}d$
and the requested point satisfies
$a\phantom{\rule{thinmathspace}{0ex}}0+b\phantom{\rule{thinmathspace}{0ex}}0+c\phantom{\rule{thinmathspace}{0ex}}z=d.$
So $z=5.$

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