A) Are perpendicular
B) Are parallel
C) \[intersect\text{ }at\text{ }an\text{ }angle\,\,45{}^\circ \]
D) \[intersect\text{ }at\text{ }an\text{ }angle\,\,60{}^\circ \]
Correct Answer: A
Solution :
[a] \[2x=3y=-z\] or \[\frac{x}{3}=\frac{y}{2}=\frac{z}{-6}\] \[6x=-y=-4z\] or \[\frac{x}{2}=\frac{y}{-12}=\frac{z}{-3}\] \[\cos \theta =\frac{{{x}_{1}}{{x}_{2}}+{{y}_{1}}{{y}_{2}}+{{z}_{1}}{{z}_{2}}}{\sqrt{{{x}^{2}}_{1}+{{x}^{2}}_{2}+{{x}^{2}}_{3}}.\sqrt{{{y}^{2}}_{1}+{{y}^{2}}_{2}+{{y}^{2}}_{3}}}\] \[=\frac{(6-24+18)}{\sqrt{{{(3)}^{2}}-{{(2)}^{2}}+{{(-6)}^{2}}}.\sqrt{2{{{{(}^{2}}+-12)}^{2}}+{{(-3)}^{2}}}}\] \[\cos \theta =0\] \[\theta =90{}^\circ \] So lines are perpendicular
You need to login to perform this action.
You will be redirected in
3 sec
