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The foot of the perpendicular drawn from...

The foot of the perpendicular drawn from origin to a plane is (4,-2,5).
(a) How far is the plane from the origin ?
(b) Find a unit vector perpendicular to that plane.
(c) Obtain the equation of the plane in general form.

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The correct Answer is:
(a) `3 sqrt(5) " (b) (4)/(3 sqrt(5)) hati - (2)/(3 sqrt(5)) hatj + (5)/(3 sqrt(5)) hatk`
(c) 4x - 2y + 5z = 35
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MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -EXERCISE 11 (E) (LONG ANSWER TYPE QUESTIONS (II) )
  1. (i) Find the distance of the point (-2,3,-4) from the line : (x + 2)...

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  2. Find the ratio in which the line-segment joining the points : (i) (2...

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  3. Find the equation of the plane passing through the point (1,2,1) and p...

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  4. Find the image of the point : (i) (2,-3,2) in the plane 2x + y - 3z ...

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  5. (i) Find the co-ordinates of foot of perpendicular drawn from the poin...

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  6. The foot of the perpendicular drawn from origin to a plane is (4,-2,5)...

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  7. Find the co-ordinates of the foot of the perpendicular Q drawn from P ...

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  8. Find the length and the foot of the perpendicular from the point P(7,1...

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  9. Find the distance of the point P (1,2,3) from its image in the plane x...

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  10. Find the coordinates of the point where the line through (3,-4,-5) and...

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  11. (i) A variable plane, which remains at a constant distance '3p' from t...

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  12. If a plane has intercepts a,b,c on axes and is at a distance of p unit...

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  13. A variable plane passes through a fixed point (a,b,c) and meets the co...

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  14. A variable plane moves in such a way that the sum of the reciprocals o...

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  15. Differentiate e^tanx cosx

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  16. Find the equations of the bisectors of the angles between the plane...

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  17. In the following determine whether the given planes are parallel or pe...

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