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## Homework Statement

Line of intersection between P1: x+y+z=7 and P2:2x-3y-z=-8 crosses the XZ plane at point A and crosses the YZ plane at point B

Find the length Of AB

Okay so first of all i`m having trouble with understanding crossing the `XZ`plane or `YZ`plane.

does this mean that A x=z=0 A(0,something,0) and B(something,0,0)

What i`m thinking to do with this problem, is finding the points A and B, an then finding vector AB and finding the magnitude, and that should be the length.

So the first thing i did was get the equation of the line..

1 x+y+z=7

2 2x-3y-z=-8

subtract eq1-eq2

-x+4y+0 = 15

x= 4y-15 (3)

sub (3) in 1

4y-15 +y + z =7

z= 22-4y

y=t

x=-15 +4t

y=t

z=22-4t

r=(-15,0,22) + t(4,1,-5) (equation of line of intersection)

so that means that the direction vector is paralell to the line segment AB

but now i`m clueless as to how to solve for A or for B... can some one give me a hintÉ