if Q is equal to 0 1 is equal distance from P is equal to 5, -3 and R is equal to X, 6 find the values of x
Answers
Answer:
Let
n⃗ =(a,b,c)=⎡⎣⎢abc⎤⎦⎥,v⃗ =(p,q,r)=⎡⎣⎢pqr⎤⎦⎥,w⃗ =(x,y,z)=⎡⎣⎢xyz⎤⎦⎥
where n⃗ is the plane normal vector, v⃗ is the point those distance L to the plane we want to find out, and w⃗ is just an example point. The equation of the plane is then
n⃗ ⋅w⃗ =d
The signed distance l between the plane and point v⃗ , in units of plane normal length, is
l=n⃗ ⋅v⃗ −d
because both d (the signed distance between origin and the plane) and l (the signed distance between the point and the plane) are measured in the same direction, n⃗ .
To find the actual distance L between the point v⃗ and the plane, we must divide the absolute value of l by the length of the normal vector n⃗ :
L=|n⃗ ⋅v⃗ −d|∥n⃗ ∥=|ap+bq+cr−d|a2+b2+c2−−−−−−−−−−√
For a more detailed derivation,