Question

The angle between the straight lines $x-1=\frac{2y+3}{3}=\frac{z+5}{2}$ and $x=3r+2;y=-2r-1;z=2$, where $r$ is a parameter, is

• A. 0
• B. ${\cos }^{-1}\left(\frac{-3}{\sqrt{182}}\right)$
• C. ${\sin }^{-1}\left(\frac{-3}{\sqrt{182}}\right)$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (D)

Equation of first line is $\frac{x-1}{1}=\frac{y+\frac{3}{2}}{\left(\frac{3}{2}\right)}=\frac{z+5}{2}$
equation of second line is $\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z-2}{0}$
cos $\theta =\frac{1.3+\left(\frac{3}{2}\right)\left(-2\right)+2.0}{\sqrt{{\left(1\right)}^2+{\left(\frac{3}{2}\right)}^2+{\left(2\right)}^2}\sqrt{{\left(3\right)}^2+{\left(-2\right)}^2+10^2}}$
cos $\theta$ = 0 $\Rightarrow$ = 90${}^{\circ }$