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In each of the following cases, determi...

In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin.(a) `z = 2` (b) `x + y + z = 1` (c) `2x + 3y z = 5`(d) `5y + 8 = 0`

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The correct Answer is:
d.c's `1,0,0`, perpendicular distance `= 2` units
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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11 D
  1. Find the normal form of the plane x+2y-2z+6=0. Also find the length o...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the value of 'lambda' if the following planes are perpendicular....

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  15. Find the equation of the plane passes through the point (2,3,5) and pa...

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  16. Find the equation of the plane passes through the point (1,-3,1) and p...

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  17. Find the equation of the plane passes through the point (2,1,-2) and p...

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  18. Equation of plane passing through the points (2, 2, 1) (9, 3, 6) and p...

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

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  20. Find the equation of the plane passing through the point (-1, 3, 2) a...

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