Question

What is the angle between the lines $\frac{x-2}{1}=\frac{y+1}{-2}=\frac{z+2}{1}$ and $\frac{x-1}{1}=\frac{2y+3}{3}=\frac{z+5}{2}=?$

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. None of the above

Answer 1

The correct option is A $\frac{\pi }{2}$

The direction ratios of the line are:

$B=(a,b,c)=(1,-2,1)$

The normal to the plane has the coordinates:

$N=(-2,1,2)$

Let the angle between the line and the plane be ${}^{\prime }{x}^{\prime }$

$\therefore ,sinx=\frac{(B.N)}{(|B|\times |N|)}$

By substuting the values we get

$sinx=1$

$i.e.x=\frac{\pi }{2}$.