Verified Solution • 2025–26 Session moderate

QJEEM19Ma390b: JEE Main 2019 Mathematics - Class 12 JEEM19Ma390b Solution: If a point R(4, y, z) lies on the line segment joining the…

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 :

Multiple Choice Options

  • A 2142 \sqrt {14}
  • B 53\sqrt {53}
  • C 2212 \sqrt {21}
  • D 6

Step-by-Step Verified Solution

Equation of PQ is

x−28−2=y+30−(−3)=z−410−4{{x - 2} \over {8 - 2}} = {{y + 3} \over {0 - \left( { - 3} \right)}} = {{z - 4} \over {10 - 4}}

⇒\Rightarrow x−26=y+33=z−46{{x - 2} \over 6} = {{y + 3} \over 3} = {{z - 4} \over 6}

Point R (4, y, z) lies on this

∴\therefore 4−26=y+33=z−46{{4 - 2} \over 6} = {{y + 3} \over 3} = {{z - 4} \over 6}

⇒\Rightarrow 13=y+33=z−46{1 \over 3} = {{y + 3} \over 3} = {{z - 4} \over 6}

y = -2 and y = 6

∴\therefore R = (4, -2, 6)

Distance of R(4, -2, 6) from the origin O(0, 0, 0) is

RO = 42+(−2)2+62\sqrt {{4^2} + {{\left( { - 2} \right)}^2} + {6^2}}

= 56=214\sqrt {56} = 2\sqrt {14}

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