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The angle between the planes represented by 2x26y212z2+18yz+2zx+xy=0 is

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a
Cos−11621
b
Cos−11721
c
Cos−11921
d
π2

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detailed solution

Correct option is A

The equation 2x2−6y2−12z2+18yz+2zx+xy=0 represents two planes and they are2x−3y+6z=0       ..........(1)x+2y−2z=0       ..........(2)If θ is the angle between the planes (1) and (2) then cosθ=|(2)(1)+(−3)(2)+6(−2)|22+(−3)2+6212+22+22=1621 ∴θ=Cos−11621Method 2:cosθ=|a+b+c|(a+b+c)2+4(f2+g2+h2−ab−bc−ca)8+4k+24=0k=−8

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