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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
214
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C
221
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D
6
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Solution

The correct option is B 214
Equation of line segment joining the points P(2,3,4) and Q(8,0,10) is
x22=y+31=z42
Any point on the line PQ is of the form (2λ+2,λ3,2λ+4)
Since, R(4,y,z) lies on the above line segment,
2λ+2=4λ=1
Thus, coordinates of R is (4,2,6)

Distance of R from the origin =(4)2+(2)2+(6)2=56=214

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