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Find the equation of the plane passing t...

Find the equation of the plane passing through (a,b,c) and paralle toteh plne `vecr.(hati+hatj+hatk)=2`.

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The correct Answer is:
`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)`.
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RS AGGARWAL-THE PLANE-Exercise 28F
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  3. Find the value of lambda for which the given planes are perpendicular ...

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  4. Find the acute angle between the following planes: 2x-y+z=5 and x+y+2...

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  5. Show that each of the following pairs of planes are at right angles: ...

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  6. Prove that the plane 2x+3y-4z=9 is perpendicular to each of the planes...

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  7. Show that the planes 2x-2y+4z+5=0 and 3x-3y+6z-1=0 are parallel.

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  8. Find the value of lambda for which the planes x-4y+lambdaz+3=0 and 2x+...

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  9. Write the equation of the plane passing through the origin and paralle...

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  10. Find the equation of the plane passing through (a,b,c) and paralle tot...

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  11. Find the equation of the plane passing through the point (1,-2,7) and ...

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  12. Find the equation of the plane passing through the point (-1,-1,2)a n ...

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  13. Find the equation of a plane passes through the point (0 ,0,0) and per...

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  14. Find the equation of the plane that contains the point A(1,-1,2) and ...

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  15. Find the equation of the plane passing through the points A(1,-1,2) an...

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  16. Find the equation of the plane passing through the points (-1,1,1) ...

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  17. Find the equation of the plane through the points A(3,4,2) and B(7,0,6...

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  18. Find the equation of the plane through the points A(2,1,-1) and B(-1,3...

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