#So i dont really understand making vector representations in R3 or higher, can someone help me?
true notch
spiral zenithBOT
terse granite
What have you done so far?
true notch
well I wanted to create a vector presentation for all the equations
but i just figured out i cant just flip the normal vector because it is in R³
terse granite
What operation gives you the cosine of the angle between two vectors
true notch
cos = u v / |u| |v| ?
terse granite
Yeah the dot product
true notch
ye exactly
terse granite
So you should take the dot of the normal and the direction vector
true notch
ye and if that is 0 it would be 90 degrees right?
terse granite
0 means it’s aligned
But remember you are using the normal, not a vector lying on the plane
true notch
oooh ye
terse granite
So it will be flipped, aligned would mean perpendicular
terse granite
V dot N = 0 would mean V (direction of the line) is perpendicular to the normal of the plane. So V must be aligned with the plane
terse granite
Yes
true notch
aaah okay thank you
do u also know
how i can change a formula like ax+by+cz=d into a vector presentation?
terse granite
Vector form of a plane will look like p = w + su + tv where w is any point on the plane and u and v are vectors that lie on the plane starting from w, not aligned with eachother
terse granite
Yes, otherwise it would collapse into a line
true notch
ye okay thank you
terse granite
So pretty much get 3 points on the plane (p1, p2 p3), choose one to be w (w=p1), then u and v will be u= p2 - p1 and v = p3 - p1. If u = cv you need to use a different p2 or p3
true notch
okay nice
I see they also use n(x-p)=0
is that only possible if the equation is =0 ?
terse granite
No that doesn’t look exclusive to eq=0 assuming its the dot product
x-p will be a vector lying on the line, which will just be c*d
So it’s essentially the same, just an extra step of choosing another point on the line
true notch
okay thats all i needed to know