A) \[30{}^\circ \]
B) \[45{}^\circ \]
C) \[60{}^\circ \]
D) \[75{}^\circ \]
Correct Answer: A
Solution :
[a] \[y-\sqrt{3}x-5=0\] line one \[\sqrt{3}y-x+6=0\] Line two \[y=mx+c\] \[y=\sqrt{3}x+5\] \[y=\frac{x}{\sqrt{3}}-\frac{6}{\sqrt{3}}\] \[{{m}_{1}}=\sqrt{3}\] \[{{m}_{2}}=\frac{1}{\sqrt{3}}\] Angle between two lines, \[\tan \theta =\left| \frac{{{m}_{1}}-{{m}_{2}}}{1+{{m}_{1}}{{m}_{2}}} \right|\] \[=\left| \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{1+\sqrt{3}\frac{1}{\sqrt{3}}} \right|=\frac{1}{\sqrt{3}}\] \[=\tan 30{}^\circ \] \[\therefore \,\,\,\theta =30{}^\circ \]
You need to login to perform this action.
You will be redirected in
3 sec
