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The vector equation of a plane is vecr.(...

The vector equation of a plane is `vecr.(6hati-3hatj-2hatk)+2 = 0`. Convert it into normal form. Also find the length of perpendicular from origin and the d.c.'s of this perpendicular vector.

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The correct Answer is:
`vecr.(-6/7hati+3/7hatj+2/7 hatk) = 2/7`, d.c's `= (-6)/(7), 3/7,2/7`, length of perpendicular `= 2/7` units
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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11 D
  1. Find the equation of the plane which is at a distance of sqrt(29) unit...

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  2. The vector equation of a plane is vecr.(hati+2hatj+2hatk) = 12. Conver...

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  3. The vector equation of a plane is vecr.(6hati-3hatj-2hatk)+2 = 0. Conv...

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  4. Find the equation of a plane which is a distance of 2 units from ori...

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  5. Find the angle between the planes vecr.(hati+hatj-2hatk)=3 and vecr.(2...

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  6. Find the vector equation of the following planes whose Cartesian equat...

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  7. The co-ordiantes of the foot of perpendicular from origin to a plane a...

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  8. Find the normal form of the plane x+2y-2z+6=0. Also find the length o...

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  9. Find the d.c.'s of the normal and length of perpendicular from origin...

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  10. In each of the following cases, determine the direction cosines of th...

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  11. Find the coordinates of the foot of the perpendicular drawn from the ...

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  12. Find the coordinates of the foot of perpendicular drawn from origin to...

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  13. Find the vector and Cartesian equation of the plane that passes throug...

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  14. Find the vector and cartesian equation of a plane which passes throug...

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  15. Find the vector equation of the following plane in non-parametric fo...

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  16. Convert the equation of the plane vecr = (hati-hatj)+lambda(-hati+hatj...

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  17. Find the vector equation of the plane passing through the points P(2\ ...

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  18. Find the equation of the plane passing through A(2, 2, -1) , B(3, 4, 2...

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  19. Find the cartesian equation of plane passing through the points (1,1,...

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  20. Find the angle between the folowing planes :- (i) vecr.(2hati-3hatj+...

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