# 3   Find the Cartesian equation of the following planes:     (a)     $\overrightarrow{r}.(\widehat{i}+\widehat{j}-\widehat{k})=2$

D Divya Prakash Singh

Given the equation of the plane $\overrightarrow{r}.(\widehat{i}+\widehat{j}-\widehat{k})=2$

So we have to find the Cartesian equation,

Any point $A (x,y,z)$ on this plane will satisfy the equation and its position vector given by,

$\vec{r}=x\widehat{i}+y\widehat{j}-z\widehat{k}$

Hence we have,

$(x\widehat{i}+y\widehat{j}+z\widehat{k}).(\widehat{i}+\widehat{j}-\widehat{k}) =2$

Or,  $x+y-z=2$

Therefore this is the required Cartesian equation of the plane.

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