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Question
The acute angle between the two planes x+y+2z = 3 and 3x -2y +2z = 7 ________.
Options
`"sin"^-1( 5/sqrt102)`
`"cos"^-1(5/sqrt102)`
`"sin"^-1(15/sqrt102)`
`"cos"^-1(15/sqrt102)`
Solution
`"cos"^-1(5/sqrt102)`
`"cos" theta = abs(("a"_1"b"_1 + "a"_2"b"_2+"a"_3"b"_3)/(sqrt("a"_1^2+"a"_2^2 +"a"_3^2)sqrt("b"_1^2 +"b"_2^2 + "b"_3^2))`
`"cos" theta = abs(((1)(3) + (1)(-2) +(2)(2))/(sqrt(1^2+1^2+2^2) sqrt(3^2 + 2^2 +2^2))) `
`= abs ((3-2+4)/(sqrt6 sqrt17))`
`= abs(5/sqrt102)`
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