Question

The angle between the lines $\frac{x-5}{1}=\frac{y-7}{2}=\frac{z-11}{3}$ and $\frac{x}{2}=\frac{y+3}{2}=\frac{z-4}{-2}$ is

• A. $90^{\circ }$
• B. $0^{\circ }$
• C. $180^{\circ }$
• D. None of these

Answer 1

Answer: (A)

The direction ratios of the lines are $a_{=}1$,
$b_1=2$,
$C_1=3$,
$a_2=2$,
$b_2=2$,
$c_2=-2$
$\therefore cos\theta =\frac{1\cdot 2+2\cdot 2+3\cdot \left(-2\right)}{\sqrt{1+4+9}\sqrt{4+4+4}}=0$
$\Rightarrow \theta =90^{\circ }$