1.

Find the angle between the planes `3x+y+2z=1` and `2x-y+z+3 = 0`.

Answer» Here `{:(a_(1)=3,b_(1)=1,c_(1)=2),(a_(2)=2,b_(2)=-1,c_(2)=1):}`
If the angle between the planes is `theta`, then
`costheta = (a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))/(sqrt(a_(1^(2))+b_(1^(2))+c_(1^(2)))sqrt(a_(2^(2))+b_(2^(2))+c_(2^(2))))`
`=(6-1+2)/(sqrt(9+1+4)sqrt(4+1+1))`
`=(7)/(sqrt(14)sqrt(6)) = (7)/(2sqrt(21))`
`rArr theta = cos^(-1)(7/(2sqrt(21)))`


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