# Find an equation of the plane passing through the point

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

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Edward Belanger

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: $$\displaystyle{2}{x}+{3}{y}-{z}={10}$$