Multivariable Calculus: Distance from a point to a plane

In this exercise, we find the distance from the point (1, 2, 3) to the plane 3x - y + 5z = 2 using geometric methods. We start by identifying another point on the plane and connect it to our given point with a vector v. We then project v onto a line perpendicular to the plane by projecting it on the normal vector n derived from the plane's equation. The distance is calculated as the absolute value of the dot product of v and n divided by the magnitude of N. This approach emphasizes understanding vector projections for solving various distance problems in geometry without relying on specific formulas. #mathematics #math #vectorcalculus #multivariablecalculus #linesandplanes #iitjammathematics #calculus3