The plane passing through the point (4, --1, 2) and parallel to the lines [x + 2 3 = y - 2…

Question

The plane passing through the point (4, --1, 2) and parallel to the lines  $${{x + 2} \over 3} = {{y - 2} \over { - 1}} = {{z + 1} \over 2}$$  and  $${{x - 2} \over 1} = {{y - 3} \over 2} = {{z - 4} \over 3}$$ also passes through the point -

Accepted Answer

Let  $$\overrightarrow n $$ be the normal vector to the plane passing through (4, -1, 2) and parallel to the lines L1 \& L2

then $$\overrightarrow n $$ = $$\left| {\begin{pmatrix} {\widehat i} & {\widehat j} & {\widehat k}  \
   3 & { - 1} & 2  \
   1 & 2 & 3  \

\end{pmatrix} } \right|$$

$$ \therefore $$  $$\overrightarrow n $$ = $$ - 7\widehat i - 7\widehat j + 7\widehat k$$

$$ \therefore $$  Equation of plane is

- 1(x - 4) - 1(y + 1) + 1(z - 2) = 0

$$ \therefore $$  x + y - z - 1 = 0

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Solutions · 1