1. ## Two Vector Problems

1. The problem statement, all variables and given/known data

Find the implicit form for the plane that contains the origin and the line:

L(t) = <1+t,1-t,2t>

3. The attempt at a solution'

So, the point P = (1,1,0) and vector v= <1,-1,2>.

For this problem, I am guessing I need to find a normal vector and use the point (1,1,0) to find the implicit equation, but how am I supposed to find another vector other than <1,-1,2> to get the normal vector?

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#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> ?

Just Checking....
2. The point $(1,1,0)$ is on the line.
Therefore, the vector $<1,1,0>$ is in the plane.
Thus the normal is $<1,1,0>\times <1,-1,2>$.