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. $2\sqrt{14}$
• B. $6$
• C. $\sqrt{53}$
• D. $2\sqrt{21}$

Answer 1

Answer: (A)

$2\sqrt{14}$

$\frac{4}{2}=\frac{-y}{y+3}=\frac{10-z}{z-4}$
$\Rightarrow z=6$ & $y=-2$
$\Rightarrow R(4,-2,6)$
dist. from origin $=\sqrt{16+4+36}=2\sqrt{14}$