Scalar Equation of a PLANE (full lesson) | MCV4U

[thedeathofbirth]

You certainly are the best teacher! Everytime I do a new lesson, it takes all the stress away after having to deal with a whole bunch of jerks at work all day. Thank you for that!

[thedeathofbirth]

Jensen, Thank you so very much! Please forgive me for the delay, I got Covid at work and still am very sick. It has been four days that I have not been able to even sit straight much less be on my computer to study. I live alone and honestly this time getting sick with Covid has been the most bizarre experience that I've had! This is the third time I got it since 2020 and this one is the nastiest! Please keep safe, the world needs people like you.... It may not much sense to you, but I live alone and dealing with this sickness has been very hard and sometimes it become very difficult to stay motivated and fight for my goals. But because of your kindness, even though you have been working hard to make videos for university Cal you took the time( time is money) to answer my question! In a few days I will start again to fight to get to engineering school. Many thanks, you are a true mentor and educator!

[amalibrahim]

You are amazing! do you have a video to teach us how to use GeoGebra the way you use it?

[thedeathofbirth]

Jensen, I am trying to visualize this but I know that I am missing something! Why is it that we treat the normal to a plane as a unique vector? Of course, it is true that there is only ONE LINE that can be perpendicular to a plane, But I get into a confusing situation when I try in my mind to move this normal on this flat surface, in my head as it moves on the plane in my 3-D space depending on the position of my plane its x or/and y, or and z coordinates change, I get a rectangular Prism when I imagine my plane with all its normals on it.
And yet It ought to remain fixed if the scalar equation for each plane is unique and defined by its normal vector! So I know I am missing something but what?! After 2 nights of thinking about this I am giving up and of course you are my metal block saviour. If you have a minute would you please tell me what my mistake is? As when I am not able to understand all aspects of a lesson I am not able to move on to the next. Thank you!
You see I could just regurgitate the rule you taught us and solve question such as testing if a given vector is parallel to a plane or not, just by taking the vectors dot product with the normal of the plane and say cool it is ZERO then yes the vector is parallel to the plane, but because I can't imagine it I can't convince myself !

[johannes]

Why do you not explain how to derive the scalar equation of a plane and why there is a relationship to the normal vector?