Question

If $,A=(3,1,-2),B$= (4, 0, -4), C = (4, -3, 3), D = (6, -2, 2)$,thentheanglebetweenthelines$AB$and$CD$ is

• A. ${30}^o$
• B. ${\cos }^{-1}\left(\frac{1}{6}\right)$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${60}^o$

Given, $A=(3,1,-2),B=(4,0,-4),C=(4,-3,3),D=(6,-2,2)$

DR of $AB=(3-4,1-0,-2+4)=(-1,1,2)$
DR of $CD=(4-6,-3+2,3-2)=(-2,-1,1)$

$\cos \theta =\frac{2-1+2}{\sqrt{1+1+4}\sqrt{4+1+1}}$

$\cos \theta =\frac{3}{6}=\frac{1}{2}$
$\therefore \theta ={60}^{\circ }$