I have got this line g : x → = ( − 1 2 0...
I have got this line
And this plane:
Now for which t is the line element of the plane?
My calculations: When I put the equation of the line in the equation of the plane i get: And this plane:
This is the same as:
And now I do not know how to go on.
The solution is t=2
Can someone explain the last step to the solution please?
Answer & Explanation
The line and the plane are parallel iff the plane's normal vector (t,1,t) and the line's direction vector (−1,4,−1) are perpendicular; this gives t=2.
As for t=2 the vector (−1,2,0) lies in the plane the whole line lies in that plane.
we have the plane and the line . Now if we have
From the second equation we have and now making hence for