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Q.

The line which passes through the origin and intersects the two lines x12=y+34=z53,x42=y+33=z44is

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a

x1=y3=z5

b

x1=y3=z5

c

None of these

d

x1=y3=z5

answer is D.

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Detailed Solution

 If the lines r¯=a¯+sb¯,r=c¯+td¯ intersect then c¯-a¯b¯d¯=0

 Let xα=yβ=zγ be the equation of required line 

-13-5243αβγ=029α-7β-10γ=0   1

4-34234αβγ=012α+4β-9γ=0  2

 From (1) and (2) α103=β141=γ200

 The line is x103=y141=z200

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