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Line of intersection between two planes?
Hi, can you help with this?
The planes 3x−5y+5z=−41 and 5x+3y+2z=−9 aren't parallel, they must intersect with line. What is the vector parametric equation for this line?
I keep getting <t, 36/5 - 19t/5, -78/5 + 16t/5> but thats wrong...
1 Answer
- JacyLv 71 decade agoFavorite Answer
Using simplex algorithm method:
x.......y........z........-1
3.......-5........5......-41......= 0
5*.......3........2......-9........= 0
___________________
....-34/5...19/5*.....-178/5...= 0
......3/5.....2/5.......-9/5..... = -x
___________________
............-35/19......-178/19..= -z
............25/19..........37/19..= -x
______________________
Hence; -x = (25/19)y - 37/19
and, ... -z = (-35/19)y + 178/19
Therefore, if we let y = t, then;
x = (-25/19)t + 37/19, ....while, z = (35/19)t - 178/19
The line of intersection is: <(-25/19)t + 37/19, t, (35/19)t - 178/19>
