Question

The cartesian equation of the plane $\overline{r}=(1+s-t)\hat{i}+(2-s)\hat{j}+(3-2s+2t)\hat{k}$

• A. $2x-y=5$
• B. $2x+z=5$
• C. $2x+y=5$
• D. $2x-z=5$

Answer 1

Answer: (B)

$2x+z=5$

$\overrightarrow{r}=(1+s-t)\hat{i}+(2-s)\hat{j}+(3-2s+2t)\hat{k}$
$\Rightarrow x\hat{i}+y\hat{j}+z\hat{k}=(1+s-t)\hat{i}+(2-s)\hat{j}+(3-2s+2t)\hat{k}$
Comparing coefficient, we get
$1+s-t=x,2-s=y,3-2s+2t=z$
$\Rightarrow s=2-y,t=1+s-x=3-y-x$
Eliminating $s$ and $t$, we get
$2x+z=5$ which is required equation of plane in cartesian form.