Question

Find the angle between the lines joining the following pairs of points :
(i) $(0,4,1),(2,3,-1)$;
(ii) $(4,5,0),(2,6,2)$

• A. the lines are parallel
• B. the lines are perpindicular
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

Answer: (A)

the lines are parallel

Direction cosines of line joining $(0,4,1),(2,3,-1)$=$(-2,1,2)$
Direction cosines of line joining $(4,5,0),(2,6,2)$=$(-2,1,2)$
Dot product of $(-2,1,2),(-2,1,2)$

$\Rightarrow (-2,1,2).(2,-1,-2)=\mathrm{3.3.}\cos \theta$
$\Rightarrow -1=\cos \theta$
$\Rightarrow \theta ={180}^o$
So, the lines are parallel.