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:

214

221

Correct option is A.
214
x−2/6=y+3/3=z−4/6=λ
x=6λ+2, y=3λ−3, z=6λ+4
4=6λ+2
λ=1/3
y=3×1/3−3=−2
z=6×1/3+4=6
R(4,−2,6)
distance=√(16+4+36)=√56=2√14