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

Find the vector equation for the line of intersection

barstr9146

13.03.2022

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

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

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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rubes08

21.01.2021

A resaraunt recommends an 18% gratuity for dinner parties over 8 people.If a group of 10 people spend $114 how much will they owe $6.33

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