Find the equation of the plane passing through (a,b,c) and paralle toteh plne `vecr.(hati+hatj+hatk)=2`.
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Correct Answer – `vecr.(hati+hatj+hatk)=a+b+c`
We know that any plane parallel to `vecr.vecn=q` is `vecr.vecn=q_(1)`.
Let the required plane parallel to the given plane be `vecr.(hati+hatj+hatk)=q_(1)`
`rArr (xhati+yhatj+zhatk).(hatk+hatj+hatk)=q_(1)`
`rArr (ahati+bhatj+chatk).(hati+hatj+hatk)=q_(1)`
`rArr q_(1)=(a+b+c)`.
Hence, the required equation is `vecr.(hati+hatj+hatk)=(a+b+c)`.