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Solution


Q.

Let the line L intersect the lines x – 2 = – y = z – 1, 2(x + 1) = 2(y –1) = z + 1 and be parallel to the line x–23=y–11=z–22. Then which of the following points lis on L          [2024]
1 (–13,–1,–1)  
2 (–13,1,–1)  
3 (–13,–1,1)  
4 (–13,1,1)  

Ans.

(2)

L1 : x–21=y–1=z–11=λ

L2 : x+1(1/2)=y–1(1/2)=z+11=μ

Any point on L1 and L2 will be of the form (λ+2,–λ,λ+1) and (μ2–1,μ2+1,μ–1) respectively.

Now direction ratios of line L are given by

< λ–μ2+3, –λ–μ2–1, λ–μ+2>

Also L is parallel to line x–23=y–11=z–22

⇒ λ–μ2+33=–λ–μ2–11=λ–μ+22

⇒ λ–μ2+3=–3λ–3μ2–3        ... (i)    2(λ–μ2+3)=3(λ–μ+2)     ... (ii)}   λ=–43,  μ=–23

∴  Points will be (23,43,–13) and (–43,23,–53)

∴  L is given by x–233=y–431=z+132

Point (–13,1,–1) will satisfy this line L.