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Zenmo
 one year ago
(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
Zenmo
 one year ago
(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

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Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2Not sure if I'm doing it correctly.

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2I 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
 one year ago
Best ResponseYou've already chosen the best response.0Looks good! next maybe let z=7, and find x, y values

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0you can let z anything

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0y = 8z/7 x = 2  z/7 z = anything

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2By letting z=7: x=1, y=8. Plugging them into the original equation of x+yz=2 to find Z: z=7.

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2(1, 8, 7) + T< 1, 8, 7> x = 1  t, y = 8 + 8t, z = 7+ 7t

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Represent 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
 one year ago
Best ResponseYou've already chosen the best response.2The solution from the book is: x = t + 2, y = 8t, z = 7t.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0that is also correct

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2Is my answer in a different format?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0your book is using a different point on the line, thats all. both equations are correct

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0both equations represent the same line

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2I see. Thanks! Did Loser66 managed to find the book answer format?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1and 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
 one year ago
Best ResponseYou've already chosen the best response.1sorry, 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
 one year ago
Best ResponseYou've already chosen the best response.1that gives you x =2t y= 8t z= 7t

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2Could you show the work on how you gotten ( x, y, z) = (2, 0, 0). I may need a quick refresher on substitution/elimination.

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.2Other than that. I'm all set for this problem! :)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1x = 2(1/7)t ok? so you get 2 for x,

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1y = (8/7)t =0 + (8/7)t, hence you get 0 for y same as z