The direction ratios of the perpendicular from the origin to a plane are 12,-3,4 and the length of the perpendicular is 5. Find the equation of the plane.

Explanation

The direction ratios of the perpendicular from the origin to a plane are 12,-3,4

Therefore ,`vec{n} =12 vec{1}-3 vec{j}+4 vec{k}`

`norm(vec{x})=sqrt{12^{2}+(-3)^{2}+4^{2}}`
`=sqrt{144+9+16}`
`=sqrt{169}`
`=13`

Here , `vec{n}=frac{vec{{n}}}{vec{{n} }}`

`=frac{12 vec{1}-3 vec{j}+4 vec{k}}{13}`

So, The Length of the perpendicular from the origin to the plane, `{d}=5`

Equation of the plane in normal form is

`r vec{n}=d`

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