Find the image of the point with position vector `3 hat i+ hat j+2 hat k` in the plane ` vec rdot(2 hat i- hat j+ hat k)=4.` Also, find the position vectors of the foot of the perpendicular and the equation of the perpendicular line through `3 hat i+ hat j+2 hat kdot`

Explanation

`\vec{\gamma}=x \hat{i}+y \hat{j}+i \hat{k}`


`\Rightarrow \vec{\gamma}(2 \hat{\imath}-\hat{\jmath}+\hat{k})=4`


`=2 x-y+z=4`.


`\frac{x-3}{2}=\frac{y-1}{-1}=\frac{z-2}{1}=\frac{-2(6-1+2-4)}{4+1+1}`


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