3D Geometry: If a point R(4,y,z) lies on the line segment joining the points… | JEE Main 2019 | Yukti Vault

Yukti Vault

JEE Main 2019 (Online) 8th April Evening ShiftQuestion 1

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 :

3D Geometry

$2\sqrt{21}$$\sqrt{53}$$6$$2\sqrt{14}$✓ Correct answer

Solution

$R=P+t(6,3,6)$ with $2+6t=4$, $t=\frac13$, so $R=(4,-2,6)$ and $|OR|=\sqrt{16+4+36}=2\sqrt{14}$.

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