A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{6}\]
D) none of these
Correct Answer: B
Solution :
Equation of planes are \[3x-4y+5z=0\] and \[2x-y-2z-5=0\] Direction ratios of these planes are \[(3,-4,5)\] and \[(2,-1,-2)\] Angle between these two planes is \[\theta ={{\cos }^{-1}}\left( \frac{3.2-4(-1)+5(-2)}{\sqrt{9+16+25}\sqrt{4+1+4}} \right)\] \[={{\cos }^{-1}}\left( \frac{6+4-10}{5\sqrt{2}.3} \right)={{\cos }^{-1}}(0)\] \[=\frac{\pi }{2}\] Note: Angles between the two planes is equal to the angle between their normals to the plane.
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