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Find the distance of a point (2, 5, 3)f...

Find the distance of a point `(2, 5, 3)`from the plane ` vecr.(6 hat i-3 hat j+2 hat k)=4`.

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The distance from the point to the plane is
`D=|(12-15-6-4)/sqrt(6^2+3^2+2^2)|`
`=13/7`
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NCERT-THREE DIMENSIONAL GEOMETRY-SOLVED EXAMPLES
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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 - 2...

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

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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 l1 and l2 given by r1= hat i+2 h...

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

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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 = 0from 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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