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If the points `(1," "1," "p)" "a n d" "(" "3," "0," "1)` be equidistant from the plane ` -> rdot(3 hat i+4 hat j-12 hat k)+13=0` , then find the value of p.

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The correct Answer is:
`p = 1 ; (7)/(3)`.
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MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -EXERCISE 11 (E) (SHORT ANSWER TYPE QUESTIONS )
  1. (i) Find the distance from (1,2,3 ) to the plane 2x + 3y - z + 2 = 0 ....

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  2. Find the angle between the planes : (i) 3 x - 6y - 2z = 7 " " ...

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  3. Angle between the planes: (i) vec(r). (hati - 2 hatj - hatk) = 1 and ...

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  4. (i) The position vectors of two points A and B are 3 hati + hatj + 2 h...

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

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  6. Find the vector and Cartesian equations of the plane which passes thro...

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  7. Find the vector and cartesian equation of the plane : (i) that passe...

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  8. Find the length of the perpendicular from the point (2,3,7) to the pla...

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  9. In the following, find the distance of each of the given points from t...

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  10. In the following, determine the direction-cosines of the normal to the...

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  11. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

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  12. In the following cases, find the co-ordinates of the foot of the perpe...

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

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  14. (i) Find the vector equation of the line passing through (1,2,3) and p...

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  15. (i) Find the equations of the plane passing through (a,b,c) and parall...

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  16. Find the vector and catesian equations of the plane containing the lin...

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  17. Find the angle between the lines x-2y+z=0=x+2y-2za n dx+2y+z=0=3x+9y+5...

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  18. Show that the line 3x - 2y + 5 = 0 , y + 3z - 15 = 0 and (x -1)/(5) =...

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  19. Find the equations of the line passing through the point (1, -2, 3) an...

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  20. Find the equation of the plane which bisects the line segment joining ...

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