Zenmo
  • Zenmo
(Give me your strength! :) Help me with this to prepare for finals soon.) Find parametric equations of their line of intersection of two planes. 3x - 4y + 5z = 6 x + y - z = 2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Zenmo
  • Zenmo
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Zenmo
  • Zenmo
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Zenmo
  • Zenmo
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Zenmo
  • Zenmo
Not sure if I'm doing it correctly.
Zenmo
  • Zenmo
I know that once the point ( X, Y, Z) is found, then I can add it to the cross product to find the set of parametric equations.
ganeshie8
  • ganeshie8
Looks good! next maybe let z=7, and find x, y values
Zenmo
  • Zenmo
where did you get z=7?
ganeshie8
  • ganeshie8
you can let z anything
ganeshie8
  • ganeshie8
y = 8z/7 x = 2 - z/7 z = anything
Zenmo
  • Zenmo
By letting z=7: x=1, y=8. Plugging them into the original equation of x+y-z=2 to find Z: z=7.
Zenmo
  • Zenmo
(1, 8, 7) + T< -1, 8, 7> x = 1 - t, y = 8 + 8t, z = 7+ 7t
Zenmo
  • Zenmo
Those are likely wrong
ganeshie8
  • ganeshie8
thats perfect!
Loser66
  • Loser66
Represent the line under matrix form, you have \[\left[\begin{matrix}x\\y\\z\end{matrix}\right]=\left[\begin{matrix}2-(1/7)z\\(8/7)z\\z\end{matrix}\right]\] ok?
Zenmo
  • Zenmo
The solution from the book is: x = -t + 2, y = 8t, z = 7t.
ganeshie8
  • ganeshie8
that is also correct
Zenmo
  • Zenmo
Is my answer in a different format?
ganeshie8
  • ganeshie8
your book is using a different point on the line, thats all. both equations are correct
ganeshie8
  • ganeshie8
both equations represent the same line
Zenmo
  • Zenmo
I see. Thanks! Did Loser66 managed to find the book answer format?
Loser66
  • Loser66
and let z =7t, hence you have \[\left[\begin{matrix}x\\y\\z\end{matrix}\right]=\left[\begin{matrix}2\\0\\0\end{matrix}\right]+\left[\begin{matrix}(1/7)7t\\(8/7)7t\\7t\end{matrix}\right]\]
Loser66
  • Loser66
sorry, the first entry is -1/7t, not 1/7 t pick t out from the far right matrix, you have required form of parametric equation. \[\left[\begin{matrix}x\\y\\z\end{matrix}\right]=\left[\begin{matrix}2\\0\\0\end{matrix}\right]+t\left[\begin{matrix}-1\\8\\7\end{matrix}\right]\]
Loser66
  • Loser66
that gives you x =2-t y= 8t z= 7t
Zenmo
  • Zenmo
Could you show the work on how you gotten ( x, y, z) = (2, 0, 0). I may need a quick refresher on substitution/elimination.
Zenmo
  • Zenmo
Other than that. I'm all set for this problem! :)
Loser66
  • Loser66
x = 2-(1/7)t ok? so you get 2 for x,
Loser66
  • Loser66
y = (8/7)t =0 + (8/7)t, hence you get 0 for y same as z
Loser66
  • Loser66
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Loser66
  • Loser66
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