https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:introduction-to-three-dimensional-geometry-ncert-new/x0419e5b3b578592a:untitled-1055/v/distance-between-2-points-in-3d 2025-05-22T11:09:14.016569349Z Distance between 2 points in 3D In this video, we derive distance formulae for 2D and 3D using Pythagoras theorem. We have one right triangle in 2D and 2 right triangles in 3D. We then practice finding distance between two points using visualisation and also using the formula. We consider one application of distane formula - proving collinearity of three points. Desmos link for the animations used in the video: https://www.desmos.com/3d/sdppjosc7k Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Distance between 2 points in 3D In this video, we derive distance formulae for 2D and 3D using Pythagoras theorem. We have one right triangle in 2D and 2 right triangles in 3D. We then practice finding distance between two points using visualisation and also using the formula. We consider one application of distane formula - proving collinearity of three points. Desmos link for the animations used in the video: https://www.desmos.com/3d/sdppjosc7k https://cdn.kastatic.org/ka-youtube-converted/p4y34xphISA.mp4/p4y34xphISA.mp4 818 Distance between two points https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:introduction-to-three-dimensional-geometry-ncert-new/x0419e5b3b578592a:untitled-1055/v/geometric-applications-of-distance-formula-in-3d 2025-05-22T11:09:14.016569349Z Geometric applications of distance formula in 3D In this video, we learn how to apply distance formula to deduce or prove statements involving geometry. We first prove that given points form a right angled triangle. We leverage the fact that Pythagoras theorem works only in right angled triangles. We then prove that given points form a parallelogram. We leverage the fact that opposite sides of a parallelogram are always equal. Desmos link for the animations used in the video: https://www.desmos.com/3d/j1hgl4we7x Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Geometric applications of distance formula in 3D In this video, we learn how to apply distance formula to deduce or prove statements involving geometry. We first prove that given points form a right angled triangle. We leverage the fact that Pythagoras theorem works only in right angled triangles. We then prove that given points form a parallelogram. We leverage the fact that opposite sides of a parallelogram are always equal. Desmos link for the animations used in the video: https://www.desmos.com/3d/j1hgl4we7x https://cdn.kastatic.org/ka-youtube-converted/cbzk6p-0bTA.mp4/cbzk6p-0bTA.mp4 455 Distance between two points https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:introduction-to-three-dimensional-geometry-ncert-new/x0419e5b3b578592a:untitled-1055/v/equation-of-set-of-points 2025-05-22T11:09:14.016569349Z Equation of set of points We work on a challenging problem of 3D in this video. We are asked to find the equation of set of points satisfying a given condition. Before we apply distance formula to deduce the condition, we try to visualise the solution set - moving from 1D to 2D to 3D thereby gaining much better intuition of the problem. Desmos link for the animations used in the video: https://www.desmos.com/3d/bb75o34w9r Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of set of points We work on a challenging problem of 3D in this video. We are asked to find the equation of set of points satisfying a given condition. Before we apply distance formula to deduce the condition, we try to visualise the solution set - moving from 1D to 2D to 3D thereby gaining much better intuition of the problem. Desmos link for the animations used in the video: https://www.desmos.com/3d/bb75o34w9r https://cdn.kastatic.org/ka-youtube-converted/ClEcp4dPIUs.mp4/ClEcp4dPIUs.mp4 451 Distance between two points https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-8-pythagorean-theorem-and-irrational-numbers/lesson-11-finding-distance-in-the-coordinate-plane/e/distance-between-two-points 2026-04-07T22:59:30.107127435Z Distance between two points Second exercise in Intro to 3D exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:introduction-to-three-dimensional-geometry-ncert-new/x0419e5b3b578592a:untitled-1055/e/distance-between-points-applications 2026-04-07T22:23:57.656416987Z Distance between points: applications Third exercise in intro to 3D exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:introduction-to-three-dimensional-geometry-ncert-new/x0419e5b3b578592a:untitled-1055/e/equation-of-set-of-points 2025-08-08T02:53:40.009522544Z Equation of set of points Equation of set of points Ashish Gupta exercise