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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?

Robert Howard
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F.O
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1 Answers1

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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?

user247327
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  • That was do usually but the I came to another example and get three values for t but I may have done something wrong, and l just wanted to confirm it.Thanks for the answering the question. – F.O Dec 05 '17 at 20:23