Question

The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is

• A. $2\sqrt{29}$
• B. 1
• C. $\sqrt{\frac{37}{29}}$
• D. $\frac{\sqrt{29}}{2}$

Answer 1

Answer: (A)

$\frac{x+7}{-6}=\frac{y-6}{7}=\frac{z-0}{1}:$
point $(-7,6,0)\text{ dr’s }-6,7,1$
$\frac{x-7}{2}=\frac{y-2}{-1}=\frac{z-6}{-1}:$
point $(7,2,6)\text{ dr’s }2,-1,-1$
Shortest distance
$=\left|\frac{\left|\begin{array}{ccc}14& -4& 6\\ -6& 7& 1\\ 2& -1& -1\end{array}\right|}{\sqrt{(-7+1{)}^2+(6-2{)}^2+(6-14{)}^2}}\right|=2\sqrt{29}$