# If the length of the perpendicular from the point $(\beta ,0,\beta )$ $(\beta \neq0)$ to the line, $\frac{x}{1}=\frac{y-1}{0}=\frac{z+1}{-1}$ is $\sqrt{\frac{3}{2}}$ ,then $\beta$ is equal to :  Option 1) 1 Option 2) 2 Option 3) -1 Option 4) -2

Let point $P(\beta ,0,\beta )$ given that length of perpendicular distance

from P to line is $\sqrt{\frac{3}{2}}$.

$\frac{x}{1}=\frac{y-1}{0}=\frac{z+1}{-1}$

$R=(\lambda ,1,-\lambda -1)$

Direction ratio of $PR=(\lambda-\beta ,1,-\lambda -\beta -1)$

PR is perpendicular to the line

$=> (\lambda -\beta )(1)+(1)0+(-1)(-\lambda -\beta -1)=0$

$=> \lambda -\beta +\lambda +\beta +1=0$

$=> \lambda =\frac{1}{2}$

$PR=\sqrt{(\lambda -\beta )^{2}+1^{2}+(-\lambda -1-\beta )^{2}}=\sqrt{\frac{3}{2}}$

$=> 2\beta ^{2}+2\beta =0$

$=>\beta =0,\beta =-1$

Correct option is (3)

Option 1)

1

Option 2)

2

Option 3)

-1

Option 4)

-2

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