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The angle between two planes x+2y+2z=3 a...

The angle between two planes `x+2y+2z=3 and -5x+3y+4z=9` is

A

`"cos"^(-1)(9sqrt(2))/(20)`

B

`"cos"^(-1)(3sqrt(2))/(5)`

C

`"cos"^(-1)(3sqrt(2))/(10)`

D

`"cos"^(-1)(19sqrt(2))/(30)`

Text Solution

Verified by Experts

The correct Answer is:
C
The direction ratios of given planes are (1,2,2) and (-5,3,4).
The angle between two planes is given by
`theta=cos^(-1)((1(-5)+2(3)+2(4))/(sqrt(1+4+4)sqrt(25+9+16)))=cos^(-1)((9)/(3*5sqrt(3)))`
`rArr" "theta=cos^(-1)((3sqrt(2))/(10))`
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