Vault Of Euclid

Distance Between a Point and a Plane

Vector spaces warmup

Find the distance between point \( P = (5, -1, 0) \) and the plane given by \( 4x + 2y - z = 3 \).
distance-point-planemultivariable-calculusanalytic-geometryplanes3d-geometrydistance-formulanormal-vectorabsolute-valuemagnitudevector-projectiongeometrylinear-algebra

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

What this problem tests

Tests the ability to extract the normal vector and constant from a plane equation and correctly apply the point-to-plane distance formula.

This is a standard introductory problem in multivariable calculus and 3D analytic geometry, often used to practice working with plane equations and normal vectors.

More on Vector spaces

← today's set