Question

Find the image of $A(2,3,2)$ in the plane $\overline{r}(1,-2,1)=5$

Answer 1

$A(2,3,3)$
Plan
$\overline{r}.\hat{i}-2\hat{j}+\hat{k})=-5$
Write in contain form
$x-2y+z=-5$
$x-2y+z+5=0$
image
$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{>-{>}_1}{C}=\frac{2(a{x}_1+b{y}_1+cz+d)}{a^2+b^2+c^2}$
$\frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-2}{1}=\frac{-2(2-6+2+5)}{1+4+1}$
$\frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-2}{1}=\frac{-2\left(3\right)}{6}$
$x-2=\frac{y-3}{-2}=\frac{z-2}{1}=-1$
$x-2=-1|\frac{y-3}{-2}=-1|z-2=-1$
$x=1y-=5z=1$
image $(1,5,1)$