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Question

Question: The angle between the planes \(3 x - 4 y + 5 z = 0\) and \(2 x - y - 2 z = 5\) is...

The angle between the planes 3x4y+5z=03 x - 4 y + 5 z = 0 and

2xy2z=52 x - y - 2 z = 5 is

A

π3\frac { \pi } { 3 }

B

π2\frac { \pi } { 2 }

C

π6\frac { \pi } { 6 }

D

None of these

Answer

π2\frac { \pi } { 2 }

Explanation

Solution

θ=cos1[6+410509]=cos1(0)=π2\theta = \cos ^ { - 1 } \left[ \frac { 6 + 4 - 10 } { \sqrt { 50 } \sqrt { 9 } } \right] = \cos ^ { - 1 } ( 0 ) = \frac { \pi } { 2 }.