# The cartesian equation of the plane $\overrightarrow{r}.(\hat i\;+\hat j-\hat k)\;=2$ is ____________.

$\begin{array}{1 1} (A)\; x+y-z-2=0 \\ (B)\; x-y-z-2=0 \\ (C)\; x+y+z+2=0 \\ (D)\; x-y-z+2=0 \end{array}$

Toolbox:
• Cartesian equation of a plane is $a(x-x_1)+b(y-y_1)+c(z-z_1)=0$ where $a,b,c$ are the direction ratios
Equation of the given plane is $\overrightarrow r.(\hat i+\hat j-\hat k)=2$-----(1)
We know $\overrightarrow r=x \hat i+y \hat j+z \hat k$
Substituting for $\overrightarrow r$ in equ(1)
=>$(x \hat i+y \hat j+z \hat k).( \hat i+ \hat j- \hat k)=2$
Applying the dot product and multiplying we get,
$x+y-z=2$
or $x+y-z-2=0$
This is the required equation of the plane