Given a vector-valued function defined by r ( t ) = ( t 3 +...
Given a vector-valued function defined by
Let denote the tangent to the curve at
Then find the equation of the line L passing through the point u=(1,−1,2),parallel to the plane 2x+y+z=0 which intersects the tangent line
The equation of the line is in the form:
Since the line is parallel to the plane,we conclude that the direction of the line is the same as the plane's,let denote the normal to the plane,then , which implies:
moreover ,which implies:
Substituting (1) and (2) into (3) follows:
So the equation of the line is :
With the parametric equation :
Since the line intersects the tangent line to the curve at a point with coordinate (2,2,3),we see that s=3/2,however substituting this to the y and z we don't get y=2 and z=3 respectively,so where was I wrong?