Equation of the plane which passes through the point of intersection of lines    and     and has the largest distance from the origin is : Option 1) Option 2) Option 3) Option 4)

S Sabhrant Ambastha

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

Point of interactionof two lines

$\frac{x-1}{3}= \frac{y-2}{1}=\frac{z-3}{2} =k$

$x= 3k+1,\, \, \, y = k+2,\, \, \, z=2k+3$

and

$\frac{x-3}{1}= \frac{y-1}{2}=\frac{z-2}{3} =l$

$x=l+3; y=2l+1; z=3l+2$

$3k+1=l+3;k+2 = 2l+1$

$3k-l=2\ and\ k-2l = -1$

$6k-2l =4$

$k-2l=-1$

$k=1, l=1$

Point is (4,3,5)

Plane  has maximum distance from origin

Option 1)

This option is incorrect

Option 2)

This option is incorrect

Option 3)

This option is correct

Option 4)

This option is incorrect

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