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Find the shortest distance between the s...

Find the shortest distance between the skew lines ⃗ r = ( ⃗ i + 2 ⃗ j + ⃗ k ) + λ ( ⃗ i − ⃗ j + ⃗ k ) and ⃗ r = ( 2 ⃗ i − ⃗ j − ⃗ k ) + η ( 2 ⃗ i + ⃗ j + 2 ⃗ k )

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V PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Find the values of p so that the lines (1-x)/3 = (7y-14)/(2p) = (z-3)/...

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  2. Show that the lines (x-5)/7=(y+2)/(-5)=z/1 and x/1=y/2=z/3 are perpend...

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  3. Find the shortest distance between the skew lines ⃗ r = ( ⃗ i + 2 ⃗ j...

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  4. Find the shortest distance between the lines: (x+1)/7=(y+1)/(-6)=(z+1)...

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  5. Find the shortest distance between the lines whose vector equations ar...

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  6. Find the shortest distance between the lines whose vector equations a...

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

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

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

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

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  11. Find the vector and cartesian equations of the plane which passes thro...

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

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

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  14. Find the vector equation of the Plane Passing through the intersection...

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

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

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

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  18. Find the distance of a point (2,5,-3) from the plane vecr .(6 hati-3 h...

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  19. Find the angle between the line (x+1)/2=y/3=(z-3)/6and the plane 10 ...

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  20. Determine the direction cosines of the normal to the plane and the dis...

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