June 10th, 2017, 03:37 AM  #1 
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  Tangent plane to surface
The questions says to find tangent plane to the surface x^2y^23z=0 that goes through A(0,01) and is parallel to line : (0,0,0)+t(2,1,2). I'm really stuck here.

June 10th, 2017, 04:03 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Well, lets see. The gradient to the surface, at point is so the tangent plane to the surface at that point is . In order that it contain the point A(0, 0, 1) we must have . The line x= 3t, y= t, z= 2t has "direction vector" <2, 1, 2>. In order that the plane be parallel to that <2, 1, 2> must be perpendicular to the normal line to the plane: we must have . And, of course, since is a point on the surface, it must satisfy the equation of the surface. We must have . Solve the three equations and for , , and . 
June 10th, 2017, 05:46 AM  #3  
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  Quote:
 
June 10th, 2017, 11:26 AM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
Quote:
 

Tags 
plane, surface, tangent 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find all points on surface whose tangent plane is parallel to given plane  Addez123  Calculus  4  November 12th, 2016 06:51 AM 
centroid of solid enclosed by surface z= y^2 , plane x=0 , x = 1 and z =1  xl5899  Calculus  17  November 1st, 2016 10:28 AM 
Tangent plane  harley05  Calculus  1  May 11th, 2014 01:23 PM 
Triangle plane surface 2m base and 3 height  rsoy  Physics  4  April 23rd, 2012 08:27 AM 
coloured plane (surface)  milko  Algebra  1  August 3rd, 2008 07:14 PM 