Vector projection on a Plane

I have 2 points

A = [1,2,3]

B = [4,5,6]

a vector is generated AB = B - A

Also, i have a plane ax+by+cz = d

How can i get points of projection of vector AB onto the Plane?

Answer 1

[KSSV]

Refer here: http://www.nabla.hr/CG-LinesPlanesIn3DB5.htm

Edit @Rik (2025-06-03): apparently the website has changed to something dodgy. Luckily, there is a capture to the Wayback Machine for this page around the time of this post: http://web.archive.org/web/20200528103000/http://www.nabla.hr/CG-LinesPlanesIn3DB5.htm

[keshav gupta]

i am having problem doing it in matlab as i am a new user

[KSSV]

A, B are 2D points....we need 3D points right?

[keshav gupta]

yes, corrected

[Walter Roberson]

I am not at all sure, but possibly the replacement document is https://www.scribd.com/document/77209019/Chapter-17-I-Lines-Planes-in-3D-ENRICH -- which requires an account to download.

Answer 2

[darova]

Here is the idea:

• is your normal vector of a plane (ax + by + cz = d). . normalize it so
• create new vector such that:
•