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$The line passing through the points (5, 1, a) and (3, b, 1) crosses the y z -plane at the point (0, \frac{17}{2}, \frac{- 13}{2}) then$

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a=2,b=8

a=4,b=6

a=6,b=4

a=8,b=2

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Correct option is C

Equation of the line passing through 5,1,a and 3,b,1 is x-52=y-11-b=z-aa-1Let x-52=y-11-b=z-aa-1=λ(say)⇒x=2λ+5, y=λ1-b+1, z=λa-1+a The line meets yz-plane at 0,172,-132 ⇒2λ+5=0, λ1-b+1=172 and λa-1+a=-132 ⇒λ=-52 and b=4, a=6

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The line passing through the points (5,1,a) and (3,b,1) crosses the yz-plane at the point 0,172,−132then

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$The line passing through the points (5, 1, a) and (3, b, 1) crosses the y z -plane at the point (0, \frac{17}{2}, \frac{- 13}{2}) then$