Find the distance between the point P (−2,0,3) and the plane π: 2x − 3y + z − 6 = 0.

Answer 1

The standard formula for this is abs(ax₁ + by₁ + cz₁ + d)/sqrt(a² + b² + c²)

Where (x₁,y₁,z₁) = (-2,0,3) and a,b,c,d are the coefficients of x, y, & z with the constant (d) (2,-3,1,-6)

S0 Distance = abs(2*-2 + (-3)*(0) + 1*3 + (-6) )/sqrt(2² + (-3)² + 1²)

Distance = abs(-7)/3.742 = 1.871