3   Find the Cartesian equation of the following planes:

     (a)     \overrightarrow{r}.(\widehat{i}+\widehat{j}-\widehat{k})=2

Answers (1)

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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