What is the equation of the plane passing through the point

What is the equation of the plane passing through the point (1-,2,3) and is perpendicular to the vector i+j-2k

Solution

Equation of plane paging through (1, -2, 3)

Perpendicular to vector i+j-2k , so it act as a normla vector

n = i+j-2k =<1 , 1, -2>

Equation of plane : n.<x-x₀ , y-y₀ , z-x₀> = 0

1(x-1) + 1(y+2) -2(z-3) = 0

x -1 + y + 2 - 2z +6 = 0

x + y -2z + 7 = 0