# Two Vector Problems

• Nov 13th 2010, 02:56 PM
r2d2
Two Vector Problems
http://bh.contextweb.com/bh/set.aspx...00&token=AYRB1
http://b.scorecardresearch.com/p?c1=...11&cv=2.0&cj=1 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....
Thanks a lot in advance!
• Nov 13th 2010, 03:06 PM
Plato
The point $\displaystyle (1,1,0)$ is on the line.
Therefore, the vector $\displaystyle <1,1,0>$ is in the plane.
Thus the normal is $\displaystyle <1,1,0>\times <1,-1,2>$.
• Nov 13th 2010, 03:14 PM
r2d2
Great! And do you think my second problem is correct/ following the correct steps?