Find an equation of the plane passing through the point

sfair24bz 2021-11-13 Answered
Find an equation of the plane passing through the point perpendicular to the given vector or line. Point: (3, 2, 2) Perpendicular to: n = 2i + 3j - k

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Expert Answer

Edward Belanger
Answered 2021-11-14 Author has 6829 answers

First, convert the vector the plane is orthogonal to to standard notation.
\(\displaystyle{2}{i}+{3}{j}-{k}={<}{2},{3},-{1}{>}\)
Plug the vector from the step above and the point we were given into the standard equation of a plane in space
\(\displaystyle{2}{\left({x}-{3}\right)}+{3}{\left({y}-{2}\right)}-{1}{\left({z}-{2}\right)}={0}\)
Simplify the equation from the step above. This is the equation of the plane asked for in the question.
\(\displaystyle{2}{x}+{3}{y}-{z}={10}\)
Result: \(\displaystyle{2}{x}+{3}{y}-{z}={10}\)

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