1. Tardigrade
  2. Question
  3. Mathematics
  4. The angle between the lines (x-5/1)=(y-7/2)=(z-11/3) and (x/2)=(y+3/2)=(z-4/-2) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Three Dimensional Geometry

Solution:

The direction ratios of the lines are $a_ = 1$,
$b_1 = 2$,
$C_1 = 3$,
$a_2 = 2$,
$b_2 = 2$,
$c_2 =-2$
$\therefore cos\,\theta=\frac{1\cdot2+2\cdot2+3\cdot\left(-2\right)}{\sqrt{1+4+9}\sqrt{4+4+4}}=0$
$\Rightarrow \theta=90^{\circ}$