Answer to Question #212981 in Analytic Geometry for Selina Shadi

Question

Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3) (5)

and has normal vector ~n =< 3, 1, −1 >.

Answer 1

P₀(1, -2, 3)

normal vector n = 3i + j - k

Position vector of point P = i - 2j + 3k

The vector form of a plane that consists of a vector r₀ and a normal vector n is given by

n . ( r - r₀) = 0

So, the required equation of plane is

(3i + j - k ) . [r - ( i - 2j + 3k ) ] = 0