A) \[90{}^\circ \]
B) \[0{}^\circ \]
C) \[30{}^\circ \]
D) \[45{}^\circ \]
Correct Answer: A
Solution :
The given equation of lines are\[2x=3y=-z\] \[\Rightarrow \] \[\frac{x}{3}=\frac{y}{2}=\frac{z}{-6}\] ?.(i) and \[6x=-y=-4z\] \[\Rightarrow \] \[\frac{x}{2}=\frac{y}{-12}=\frac{z}{-3}\] ?(ii) Let \[\theta \]be the angle between these two lines. \[\therefore \] \[\cos \theta =\frac{(2)(3)+(2)(-12)+(-6)(-3)}{\sqrt{9+4+36}\sqrt{4+144+9}}\] \[=\frac{6-24+18}{7\sqrt{157}}=0\] \[\Rightarrow \] \[\theta =90{}^\circ \]
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