Maharashtra State BoardHSC Arts 12th Board Exam
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Find the Angle Between the Planes r(2i+j-k)=3 - Mathematics and Statistics

Find the angle between the planes `bar r.(2bar i+barj-bark)=3 and bar r.(hati+2hatj+hatk)=1`

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Solution

Given planes are:

`barr.(2hati+hatj-hatk)=3 and bar r.(hati+2hatj+hatk)=1`

The angle between two planes with direction ratios,

`(a_1,b_1,c_1) ` and `(a_2,b_2,c_2) ` is

`costheta=(a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2) sqrt(a_2^2+b_2^2+c_2^2))`

`costheta=(2xx1+1xx2-1xx1)/(sqrt(2^2+1^2+(-1)^2) sqrt (1^2+2^2+1^2))`

`costheta=3/(sqrt6.sqrt6)`

`costheta=3/6`

`costheta=1/2`

`costheta=cos(pi/3)`

`theta=pi/3`

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