Question

Find the cartesian form of the equation of the plane $\overline{r}.\left[\right(s+t)\hat{i}+(2+t)\hat{j}+(3s+2t\left)\hat{k}\right]=15$ where $s$ and $t$ are parameters

Answer 1

$\overrightarrow{r}.\left[\right(s+t)\hat{i}+(2+t)\hat{j}+(3s+2t\left)\hat{k}\right]=15$

$\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$

Therefore,

$(x\hat{i}+y\hat{j}+z\hat{k}).\left[\right(s+t)\hat{i}+(2+t)\hat{j}+(3s+2t\left)\hat{k}\right]=15$

$x(s+t)+y(2+t)+z(3s+2t)=15$

This is the required cartesian equation of the plane.