Browse Questions

# The angle between the lines $\large\frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1}\:\:and\:\:\large\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2}$ is?

$\begin{array}{1 1} 0 \\ \frac{\pi}{6} \\ \frac{\pi}{4} \\ \frac{\pi}{2} \end{array}$

Toolbox:
• Angle between the two lines is given by $cos\theta=\large\frac{(d.r.\:\:of\:line\:1).(d.r.\:\:of\:line\:2)}{|d.r.\:of \:line\:1|\:|d.r.\:\:of\:line\:2|}$
$d.r.$ of line (i) is $(-1,2,1)$ and that of line (ii) is $(4,1,2)$
$\therefore\:$ Angle between them is $cos\theta=\large\frac{(-1,2,1).(4,1,2)}{\sqrt {1+4+1}\sqrt {16+1+4}}$
$\Rightarrow\:cos\theta=0$ $\therefore\:\theta=\large\frac{\pi}{2}$