Find the vector equation of a plane which is at a distance of 5 units from the origin and which is normal to the vector ` hat i-2 hat j-2 hat kdot`

Explanation

When equation of plance is `a x+b y+c z+d=0`


Vector is : ` a hat{i}+b hat{j}+c hat{k}`


`d =frac{|d|}{sqrt{a^{2}+b^{2}+c^{2}}} `


`a =1 quad b =-2 quad c=-2`


`d =frac{|d|}{sqrt{1+4+4}} `


`s =frac{|d|}{3}`


`|d| =15`


Equation` rightarrow vec{r} cdot(hat{i}-2 hat{j}-2 hat{k})=15.`