Find the length and the foot of perpendicular from the point `(1,3//2,2)` to the plane `2x-2y+4z+5=0.`

Explanation

Equation of the given plane is
`2x−2y+4z+5=0……(i)`

`⇒n=2i−2j+4k`

So, the equation of line through `(1,3/2​,2)`
and parallel to n

is given by

`(x−1)/2​=−(y−3/2)/2​=(z−2)/2​=lambda`

`⇒x=2lambda+1,y=−2lambda+3/2`​ and `z=4lambda+2`

If this point lies on the given plane, then

`2(2lambda+1)−2(−2lambda+3/2​)+4(4lambda+2)+5=0`

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