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Consider the lines L₁: $\frac{x - 7}{3} = \frac{y - 5}{2} = \frac{z - 3}{1}$ and L₂: $\frac{x - 1}{2} = \frac{y + 1}{4} = \frac{z + 1}{3}$ .If a line L whose direction ratios are 2,2 and 1 intersect the lines L₁and L₂ at A and B, the distance AB equals

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answer is 3.

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Detailed Solution

$\frac{3 λ - 3 μ + 6}{2} = \frac{2 λ - 4 μ + 6}{2} = \frac{λ - 3 μ + 4}{1}$

For last two $λ - 3 μ + 3 = λ - 3 μ + 4$

$μ=1 \Rightarrow point B (3,3,2)$

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Using $μ=1$ in $3 λ -2 μ +6=2 λ -4 μ +6$

$3 λ +4=2 λ + 2 \Rightarrow λ = - 2$
Hence A(1,1,1)
$A B = \sqrt{4 + 4 + 1} = 3$

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