The line passing through the points (5,1,a)\; and\; (3,b,1)\; crosses the yz-plane at the point \left ( 0,\frac{17}{2},\frac{-13}{2} \right ).  Then

  • Option 1)

    a=8,b=2

  • Option 2)

    a=2,b=8

  • Option 3)

    a=4,b=6

  • Option 4)

    a=6,b=4

 

Answers (1)
D Divya Saini

As we learnt in 

Cartesian eqution of a line -

The equation of a line passing through two points A\left ( x_{0},y_{0},z_{0} \right )and parallel to vector having direction ratios as \left ( a,b,c \right )is given by

\frac{x-x_{0}}{a}= \frac{y-y_{0}}{b}= \frac{z-z_{0}}{c}

The equation of a line passing through two points A\left ( x_{1},y_{1},z_{1} \right )\, and \, B\left ( x_{2},y_{2},z_{2} \right ) is given by

\frac{x-x_{1}}{x_{2}-x_{1}}= \frac{y-y}{y_{2}-y_{1}}=\frac{z-z_{1}}{z_{2}-z_{1}}

- wherein

 

 Equation of line is

\frac{x-5}{2}= \frac{y-1}{1-b}= \frac{z-a}{a-1}= \lambda

If it crosses y-z plane, x=0

2\lambda +5=0 \, \, \, = > \lambda =\frac{-5}{2}

y=\lambda \left ( 1-b \right )+1=\frac{17}{2}\, \Rightarrow b= 4

z=\lambda(a-1)+a=\frac{-13}{2}

\Rightarrow a = 6


Option 1)

a=8,b=2

Incorrect Option

Option 2)

a=2,b=8

Incorrect Option

Option 3)

a=4,b=6

Incorrect Option

Option 4)

a=6,b=4

Correct Option

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