Question

find the equation of line passing throw the point (3,1,2) and 1 to the plane $\overrightarrow{r}(2i-j+k)=4$. find also the p of interaction of this line and the plane .

Answer 1

We have,

$\frac{x-3}{2}=\frac{y-1}{-1}=\frac{z-2}{1}$

Equation of line three $(3,1,2)$ & $\perp$ to plane

$\begin{array}{c}\overrightarrow{r}.\left(2\hat{i}-\hat{j}+\hat{k}\right)=4\\ 2x-y+z=4\\ \left(2r+3,-r+1,r+2\right)\end{array}$

prove that of intersection of line and plane.

$\begin{array}{c}2\left(2r+3\right)-\left(-r+1\right)+r+2=4\\ 6r+7=4\\ r=\frac{-1}{2}\\ \left(2,\frac{3}{2},\frac{3}{2}\right)\end{array}$

Then,

We get $\left(2,\frac{3}{2},\frac{3}{2}\right)$