Mixing
Finding the range of the parameter after parameterizing a line segment or a curve
$begingroup$
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?
line-integrals
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
asked Dec 5 '17 at 18:07
FarhanFarhan
597
$endgroup$
add a comment |
$begingroup$
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?
line-integrals
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
asked Dec 5 '17 at 18:07
FarhanFarhan
597
$endgroup$
add a comment |
$begingroup$
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?
line-integrals
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
asked Dec 5 '17 at 18:07
FarhanFarhan
597
$endgroup$
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?
line-integrals
line-integrals
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
asked Dec 5 '17 at 18:07
FarhanFarhan
597
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
asked Dec 5 '17 at 18:07
FarhanFarhan
597
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
edited Dec 5 '17 at 18:38
Robert Howard
2,0001825
2,0001825
asked Dec 5 '17 at 18:07
FarhanFarhan
597
asked Dec 5 '17 at 18:07
FarhanFarhan
597
asked Dec 5 '17 at 18:07
FarhanFarhan
597
597
add a comment |
add a comment |
1 Answer
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$begingroup$
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?
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
$endgroup$
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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?
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
$endgroup$
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
add a comment |
$begingroup$
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?
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
$endgroup$
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
add a comment |
$begingroup$
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?
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
$endgroup$
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?
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
answered Dec 5 '17 at 18:20
user247327user247327
11.1k1515
11.1k1515
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
add a comment |
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
$begingroup$
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.
$endgroup$
– Farhan
Dec 5 '17 at 20:23
add a comment |
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