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Question

If the lines x1=y2=z3, x13=y21=z34 and x+k3=y12=z2h are concurrent then

A
h=2,k=6
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B
h=12,k=2
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C
h=6,k=2
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D
h=2,k=12
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Solution

The correct option is B h=2,k=12
Given, L1:x1=y2=z3-------(i)
L2:x13=y21=z34-------(ii)
L3:x+k3=y12=z2λ-------(iii)
Any point on L1 is
(λ1,2λ,3λ1)
Any point on L2 is
(3λ2+1,λ2+2,4λ2+3)
λ1=3λ2+1,2λ1+λ2=2

2λ16λ2=2
2λ1+λ2=2––––––––––––
λ2=0

λ1=1
P(1,2,3)
L3 posses through P
1+k3=212=32h

1+K=32,12=1h

k=12 h=2

h=2,K=12

1232970_1189311_ans_44aade2141ea44f798fbe74591f03e80.png

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