A line with direction cosines proportional to 2, 1, 2 meets each of the lines 
and 
. The co-ordinates of each of the points of intersection are given by
Text Solution
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Given lines are 
(say)
∴ ∴ Point is P ( λ λ , λ λ – a , λ λ )
and 
i.e. 
(say)
∴ ∴ Point Q (2 μ μ – a , μ μ , μ μ )
Since d.r.’s of given lines are 2, 1, 2 and
d.r.’s of PQ = (2 μ μ – a – λ λ , μ μ – λ λ + a , μ μ – λ λ )
According to question, 
Then 
, μ μ = a .
Therefore, points of intersection are P (3 a , 2 a , 3 a ) and
Q ( a , a , a ).
Alternative method : Check by option 
i.e. 
⇒ ⇒ a = a = a and 
i.e. 
⇒ ⇒ a = a = a .
Hence is correct
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