Question

The length of the perpendicular from $\left(1,0,2\right)$ on the line $\frac{x+1}{3}=\frac{y-2}{-2}=\frac{z+1}{-1}$ is

• A. $\frac{3\sqrt{6}}{2}$ units
• B. $\frac{6\sqrt{3}}{5}$ units
• C. $3\sqrt{2}$ units
• D. $2\sqrt{3}$ units

Answer 1

Answer: (A)

Direction ratios of $PR\to 3\lambda -2,-2\lambda +2,-\lambda -3$
Direction Ratios of the line $QR\to 3,-2,-1$
Since, they are perpendicular
$3\left(3\lambda -2\right)-2\left(-2\lambda +2\right)-1\left(-\lambda -3\right)=0$
$9\lambda -6+4\lambda -4+\lambda +3=0$
$14\lambda =7$
$\lambda =\frac{1}{2}$
$R\to \left(\frac{1}{2},1,-\frac{3}{2}\right)$
$PR=\sqrt{{\left(1-\frac{1}{2}\right)}^2+{\left(0-1\right)}^2+{\left(2+\frac{3}{2}\right)}^2}$
$=\sqrt{\frac{1}{4}+\frac{4}{4}+\frac{49}{4}}$
$=\sqrt{\frac{54}{4}}$
$=\frac{3\sqrt{6}}{2}$ units