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Question

Solve :
x31=y+21=z11;x2=z+33,y=1

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Solution

L1
x31=y+21=z11 and
L2
x2=z+33,y=1
intersection of L1 and L2
x31=y+z1=z11=t
x=t+3,y=t+z,z=t+1
point on L1 can be represented as (t+3,t2,t+1)
x2=z+33=p y=1
x=2p z=3p3
point on L2 can be represented as (2p,1,3p3)
for there to be an intersection point.
t+3=2p t2=1 t+1=3p=3
1+3=2p t=1
p=1
intersection point (x,y,z)
=(t+3,t2,t+1)
=(1+3,12,1+1)
intersectionpoint=(2,1,0)

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