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Find the distance between the parallel p...

Find the distance between the parallel planes, ` vec r = dot(2 hat i-3 hat j+6 hat k)=5 a n d vec r = dot(6 hat i-9 hat j+18 hat k)+20=0.`

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`5/3`
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Find the distance between the parallel planes, vec r.(2 hat i-3 hat j+6 hat k)=5 a n d vec r.(6 hat i-9 hat j+18 hat k)+20=0.

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Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=5\ a n d\ vec rdot(( hat i-2 hat j+2 hat k)=9.

Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.

Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

Find the equation of a plane through the intersection of the planes vec rdot( hat i+3 hat j- hat k)=5a n d vec rdot(2 hat i- hat j+ hat k)=3 and passing through the point (2,1,-2)dot

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=(2 hat i- hat j- hat k)+mu(2 hat i+ hat j+2 hat k)

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Find the shortest distance between the lines vec r=(4 hat i- hat j)+lambda( hat i+2 hat j-3 hat k)a n d vec r=( hat i- hat j+2 hat k)+mu(2 hat i+4 hat j-5 hat k)dot .

Show that the following planes are at right angle: vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.

NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11 E
  1. The equation of the line passing through (1, 2, 3) and parallel to the...

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  2. Find the perpendicular distance from the point (2hati-hatj+4hatk) to t...

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  3. Find the perpendicular distance from the point (2hati+hatj-hatk) to th...

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  4. Find the distance of the point (21,0) from the plane 2x+y+2z+5=0.

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  5. Find the distance of each of the following points from the correspondi...

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  6. If the points (1,1,lamda) and (-3, 0,1) are equidistant from the plan...

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  7. Find the distance between the parallel planes 2x-y+3-4=0\ a n d\ 6x-3y...

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  8. Find the distance between the parallel planes, vec r = dot(2 hat i-3 ...

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  9. Find the equations of the planes parallel to the plane x-2y+2z-3=0 whi...

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  10. Find the length of the foot of the perpendicular from the point (1,1,2...

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  11. Find the coordinates of the foot of the perpendicular from the point ...

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  12. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

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  13. Find the image of the point O(0,0,0) in the plane 3x+4y-6z+1=0

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  14. A variable plane which remains at q constant distance 3p from the orig...

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  15. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  16. Find the distance of the point (0.-3. -2) from the plane x + 2y - z = ...

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  17. Find the equation of the plane passing through the intersection of the...

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  18. Find the equation of the plane through the intersection of the planes ...

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  19. Find the equation of a line passing through the point (2hati-3hatj-5h...

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  20. Find the vector equation of a plane which is at a distance of 5 units ...

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