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Jbreezy
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Homework Statement
The points A,B,C, D with position vectors a,b,c,d are coplanar. Given : ∠ BAC = θ
(a) Find an expression for a unit normal of this plane.
(b) Find an expression for the distance of this plane from the origin
(c) Prove that
[abd] + [bac] + [cdb] + [dca] = 0
Homework Equations
The Attempt at a Solution
So, I did part a and b but I'm just having a doubt. I'm wondering why I was given ∠ BAC = θ I didn't do part c yet so maybe it comes in there.
(a) Find an expression for a unit normal of this plane.
First I found two vectors on the plane then I crossed them. I chose to use a,b,c.
So I did
(b-a) = u = (<ux, uy,uz>
(c-a) = v = (<vx, vy,vz>
I did u cross v =
< (uyvz-vyuz)-(uxvz- vxuz) + (uxvy-vxuy) >
Lastly I just took u cross v and divided it by its own norm.
< (uyvz-vyuz)-(uxvz- vxuz) + (uxvy-vxuy) > / √(< (uyvz-vyuz)2-(uxvz- vxuz)2 + (uxvy-vxuy)2 >
Call the unit vector that I just got r(hat) then for part b all I did was to do r(hat) dot a
I could of chosen any of the other position vectors to dot with because the question says that they all lie in the same plane and all I need is a vector in that plane right? So once again why
∠ BAC = θ
Thanks