- #1
Loppyfoot
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- 0
Homework Statement
Find the implicit form for the plane that contains the origin and the line:
L(t) = <1+t,1-t,2t>
The Attempt at a Solution
'So, the point P = (1,1,0) and vector v= <1,-1,2>.
To find the implicit equation for the plane using the form ax + by + cz = d , I will substitute the vector values in for a, b, and c. So I get
x -y + 2z = d.
My question is, should I use the origin points, (o,o,o) and substitute them in for x,y, and z to get d=0, or is there another process to this?
__________________________________________________________________________________________________________________#2. The function f(t) = (t^@,1/t) represents a curve in the plane parametrically. write an equation in parametric form for the tangent line to this curve at the point where t= 2.
So I solve the gradient: <2t, -1/(t^2)> and at t=2 the point is (4, 1/4).
and the gradient normal to t=2 is <4,-1/4>.
So would the parametric equation be (4,1/4) +t<4,-1/4> ?
Thanks a lot in advance!