The equation represents a plane passing through a point having position vector \(\bar{a}\) and parallel to vectors \(\bar{b}\) and \(\bar{c}.\)
The vector equation of the plane passing through A(\(\bar{a}\)) and parallel to \(\bar{b}\) and \(\bar{c}\) is
∴ the vector equation of the given plane is
If \(\bar{r} = x\hat{i} + y\hat{j} + z\hat{k},\) then this equation becomes
This is the cartesian equation of the required plane.