Question

The distance of the point $3\hat{i}+5\hat{k}$ from the line parallel to vector $6\hat{i}+\hat{j}-2\hat{k}$ and passing through the point $8\hat{i}+3\hat{j}+\hat{k}$

• A. $2$ $units$
• B. $3$ $units$
• C. $4$ $units$
• D. $5$ $units$

Answer 1

The correct option is B $3$ $units$

$\begin{array}{c}\frac{x-8}{6}=\frac{y-3}{1}=\frac{z-1}{-2}\\ DirectionratioofAB=\left(6r+5,r+3,-2r-4\right)\\ 6\left(6r+5\right)+r+3+2\left(2r+4\right)=0\\ 41r+41=0\\ r=1\\ B=\left(2,2,3\right)\\ AB=\sqrt{1+4+4}=3\\ Hence,theoptionBisthecorrectanswer.\end{array}$