The foot of the perpendicular drawn from the origin O to a plane is N(12,-4,-3). Find the equation of the plane in cartesian form and vector form.

Explanation

`(r - bar A).OA = 0`

`(vec r - (12 hat i - 4 hat j - 3 hat k))*(12 hat i - 4 hat j - 3 hat k) = 0`

`vec r * (12 hat i - 4 hat j - 3 hat k) = |12 hat i - hat j - 3 hat k|^2`

`vec r (12 hat i - 4 hat j - 3 hat k ) = 169 `

it is in the form of vector

so , in cartesian form

`(x hat i + y hat j + z hat k)*(12 hat i - 4 hat j - 3 hat k) = 169` answer