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dezoksy [38]
3 years ago
12

Find the vector equation for the line of intersection of the planes 5x+3y−2z=−45x+3y−2z=−4 and 5x+5z=0

Mathematics
1 answer:
olga_2 [115]3 years ago
8 0

5x+5z=0\implies x+z=0\implies z=-x


5x+3y-2z=7x+3y-2x-2z=7x+3y-2=-4\implies7x+3y=-2


Letting x=t and z=-t, we have


7t+3y=-2\implies y=-\dfrac73t-\dfrac23


so the intersection is given by


\mathbf r(t)=\left(t,-\dfrac73t-\dfrac23,-t\right)

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