If a point R\left ( 4,y,z \right ) lies on the line segment joining the points P\left ( 2,-3,4 \right ) and Q\left ( 8,0,10 \right ), then distance of R from the origin is : 

  • Option 1)

    2\sqrt{14}

  • Option 2)

    2\sqrt{21}

  • Option 3)

    6

     

  • Option 4)

    \sqrt{53}

Answers (1)


P(2,-3,4)

Q(8,0,10)

R(4,y,z)

Direction Ratio of PQ= (6,3,6)

Direction ratio of PR= (2,y+3,z-4)

P,R and Q lie on same line 

\frac{6}{2}=\frac{3}{y+3}=\frac{6}{z-4}

y=-2\: \: ,\: z=6

Point R=\left ( 4,-2,6 \right )

Distance from origin 

\sqrt{16+4+36}=\sqrt{56}

=2\sqrt{14}


Option 1)

2\sqrt{14}

Option 2)

2\sqrt{21}

Option 3)

6

 

Option 4)

\sqrt{53}

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