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Question

The distance of the point P(2,3,4) from the line x+23=2y+34=3z+45 measured parallel to the plane 4x+12y3z+1=0 is d, then the value of (2d8) is

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Solution


Line through point P(2,3,4) and parallel to the given line x+23=2y+34=3z+45 is x+23=y+322=z+4353=λ
Any point on this line is Q[3λ2,2λ32,53λ43]

Direction ratios of PQ are [3λ,4λ92,5λ+83]
Now PQ is parallel to the given plane 4x+12y3z+1=0

Hence, line is perpendicular to the normal to the plane.
Thus, 4(3λ)+12(4λ92)3(5λ+83)=0
or λ=2
Q(4,52,2)
PQ=(6)2+(523)2+(6)2=172

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