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

1. Zenmo

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2. Zenmo

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3. Zenmo

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4. Zenmo

Not sure if I'm doing it correctly.

5. 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.

6. ganeshie8

Looks good! next maybe let z=7, and find x, y values

7. Zenmo

where did you get z=7?

8. ganeshie8

you can let z anything

9. ganeshie8

y = 8z/7 x = 2 - z/7 z = anything

10. 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.

11. Zenmo

(1, 8, 7) + T< -1, 8, 7> x = 1 - t, y = 8 + 8t, z = 7+ 7t

12. Zenmo

Those are likely wrong

13. ganeshie8

thats perfect!

14. 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?

15. Zenmo

The solution from the book is: x = -t + 2, y = 8t, z = 7t.

16. ganeshie8

that is also correct

17. Zenmo

Is my answer in a different format?

18. ganeshie8

your book is using a different point on the line, thats all. both equations are correct

19. ganeshie8

both equations represent the same line

20. Zenmo

I see. Thanks! Did Loser66 managed to find the book answer format?

21. Loser66

and let z =7t, hence you have $\left[\begin{matrix}x\\y\\z\end{matrix}\right]=\left[\begin{matrix}2\\0\\0\end{matrix}\right]+\left[\begin{matrix}(1/7)7t\\(8/7)7t\\7t\end{matrix}\right]$

22. 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. $\left[\begin{matrix}x\\y\\z\end{matrix}\right]=\left[\begin{matrix}2\\0\\0\end{matrix}\right]+t\left[\begin{matrix}-1\\8\\7\end{matrix}\right]$

23. Loser66

that gives you x =2-t y= 8t z= 7t

24. 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.

25. Zenmo

Other than that. I'm all set for this problem! :)

26. Loser66

x = 2-(1/7)t ok? so you get 2 for x,

27. Loser66

y = (8/7)t =0 + (8/7)t, hence you get 0 for y same as z

28. Loser66

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29. Loser66

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