Equation of a Line Passing through Two Given Points
If a point R4...
Question
If a point R(4,y,z) lies on the line segment joining the points P(2,−3,4) and Q(8,0,10), then the distance of R from the origin is :
A
√53
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B
2√14
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C
2√21
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D
6
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Solution
The correct option is B2√14 Equation of line segment joining the points P(2,−3,4) and Q(8,0,10) is x−22=y+31=z−42
Any point on the line PQ is of the form (2λ+2,λ−3,2λ+4)
Since, R(4,y,z) lies on the above line segment, ∴2λ+2=4⇒λ=1
Thus, coordinates of R is (4,−2,6)
Distance of R from the origin =√(4)2+(−2)2+(6)2=√56=2√14