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Q.

If a line with direction ratios 2 : 2: 1 intersects the line $\frac{x - 7}{3} = \frac{y - 5}{2} = \frac{z - 3}{1}$ and $\frac{x - 1}{2} = \frac{y + 1}{4} = \frac{z + 1}{3}$ at A and B then AB=.

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a

2

b

3

c

$\sqrt{3}$

d

$\sqrt{2}$

answer is D.

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Detailed Solution

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$A (7 + 3 α, 5 + 2 α, 3 + α), B (1 + 2 β, - 1 + 4 β, - 1 + 3 β)$

$Dr's of A B are 2:2:1$

$\frac{6 + 3 α - 2 β}{2} = \frac{3 + α - 2 β}{1} = \frac{4 + α - 3 β}{1}$

$α = - 2, β = 1$

$A (1, 1, 1) B (3, 3, 2)$

$A B = 3$

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If a line with direction ratios 2 : 2: 1 intersects the line x−73=y−52=z−31 and x−12=y+14=z+13 at A and B then AB=.