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Find the distance of the plane 2x - 3y +...

Find the distance of the plane `2x - 3y + 4z - 6 = 0 `from the origin.

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To find the distance of the plane given by the equation \(2x - 3y + 4z - 6 = 0\) from the origin, we can use the formula for the distance \(D\) from a point \((x_1, y_1, z_1)\) to a plane given by the equation \(Ax + By + Cz + D = 0\): \[ D = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}} \] ### Step-by-step solution: ...
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NCERT ENGLISH-THREE DIMENSIONAL GEOMETRY-SOLVED EXAMPLES
  1. Find the direction cosines of the line passing through the two points...

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  2. If a line has direction ratios 2,1,2.determine its direction cosines.

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  3. If a line makes angle 90^@, 60^@and 30^@with the positive direction ...

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  4. Find the angle between the pair of lines given by vecr=3 hat i+2 ha...

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  5. The Cartesian equation of a line is (x+3)/2=(y-5)/4=(z+6)/2. Find th...

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  6. Show that the lines (x+3)/(-3)=(y-1)/1=(z-5)/5and (x+1)/(-1)=(y-2)/2=(...

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  7. Find the vector equation of the plane passing through the intersectio...

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  8. Find the angle between the two planes 3x - 6y + 2z = 7and 2x + 2y-2z ...

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  9. Find the angle between the two planes 2x + y-2z = 5and 3x- 6y-2z = 7...

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  10. Find the distance of a point (2, 5, 3)from the plane vecr.(6 hat i-...

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  11. Find the angle between the pair of lines (x+3)/3=(y-1)/5=(z+3)/4and (x...

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  12. Find the shortest distance between the lines l1 and l2 whose vector ...

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  13. Find the distance between the lines l1and l2given by vec r= hat i+2 ...

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  14. Find the vector equation of the plane which is at a distance of 6/(sqr...

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  15. Find the direction cosines of the unit vector perpendicular to the pla...

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  16. Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin.

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

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  18. Find the vector and cartesian equations of the plane which passes thr...

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  19. Find the vector equations of the plane passing through the points R(2...

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  20. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y...

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