# The distance of the point (1, 0, 2) from the line point of intersection of the line      and the plane  ,  is: Option 1) Option 2) Option 3) Option 4)

As we learnt in

Intersection of line and plane -

Let the line

$\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}$ plane

$a_{1}x+b_{1}y+c_{1}z+d=0$ intersect at P

to find P assume general point on line as $\left ( x_{1}+\lambda a_{1}y_{1} +\lambda b_{1}z_{1}+\lambda c_{1}\right )$

now put it in plane to find $\lambda$,

$a_{1}\left ( x_{1}+\lambda a \right )+b_{1}\left ( y_{1}+\lambda b \right )+c_{1}\left ( z_{1}+\lambda c \right )+d=0$

-

Point of intesection of line

$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}=k$

x=3k+2, y=4k-1,z=12k+2

x-y+z=16

3k+2-4k+1+12k+2=16

11k-11$\Rightarrow$    k=1

Point is (5,3,14)

Distance between (5,3,14) and (1,0,2)

is $\sqrt{4^{2}+3^{2}+12^{2}}=13$

Option 1)

This is incorrect option

Option 2)

This is incorrect option

Option 3)

This is incorrect option

Option 4)

This is correct option

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