Find the equation of the plane that satisfies the stated conditions.by faslickit Tags: calculus, multivariable 

#1
Feb2209, 01:31 PM

P: 3

The plane that contains the line x = 2 + 3t, y = 4 + 2t, z = 3  t and is perpendicular to the plane x  2y + z = 5.




#2
Feb2209, 01:35 PM

P: 3

Nevermind, I kinda just solved it myself.
All good. 



#3
Feb2209, 06:49 PM

P: 2

Find the equation of the plane (if you dare) that is tangent to the following spheres:
sphere 1: r=2 center P(2,2,2) sphere 2: r=3 center Q(3,4,5) Ok, I know that the plane will be parallel to the vector PQ = <1,2,3> For the equation of a plane I need a normal vector, and a point on the plane. I know that one of the points on the plane will be one of the points on the sphere (either sphere will do, right?). The equations for the spheres are: (x2)^2 + (y2)^2 + (z2)^2=4 and (x3)^2 + (y4)^2 + (z5)^2=9 What i am thinking now is that i should take the midpoint between the spheres' centers. Use that to find another vector parallel to the plane in question, and then generate a normal vector from that  is this correct thinking? And from there, i am unsure how to find a point common to the plane and the sphere (either sphere). I have drawn this out on paper and understand the geometry... 


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