I have these two planes: $x-y-z=0$ and $x+y+2z=o$ and I want to parameterize the line of intersection which is $x=3y$ to calculate the line integral from the origin to the point $(3,1,-2)$.
$$\text{Parameterization: }\ x=3t,\, y=t,\, z=-2t$$
Here and for other problems also how I will find again the range of the parameter?
If you really understand what "parametric equations" are, this would be obvious. The origin, (0, 0, 0), corresponds to t such that x= 3t= 0, y= t= 0, z= -2t= 0. What value of t satisfies all three of those? Similarly, the point, (3, 1, -2) corresponds to x= 3t= 1, y= t= 1, and z= -2t= -2. What value of t satisfies all three of those?