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Find the shortest distance between the lines `vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk)` and `vecr=-4hati-hatk+mu(3hati-2hatj-2hatk)`

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Find the shortest distance between the lines vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)

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Find the shortest distance between the lines vecr=(-hati+5hatj)+lambda(-hati+hatj+hatk) and vecr=(-hati-3hatj+2hatk)+mu(3hati+2hatj+hatk)

Find the angle between the lines vecr=hati-hatj+hatk+lambda(2hati-2hatj+hatk) and vecr=2hati-hatj+2hatk+mu(hati+hatj+2hatk) .

Find the angle between the pair of lines given by vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk)

Find the shortest distance between the lines whose vector equations are vecr=(hati+2hatj+3hatk)+lambda(hati-3hatj+2hatk) and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

Find the angle between the line vecr=(2hati+2hatj+hatk)+lambda(2hati-3hatj+2hatk) and the plane vecr.(3hati-2hatj+5hatk)=4

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NEW JOYTHI PUBLICATION-THREE DIMENSIONAL GEOMETRY-Ncert Miscellaneous Exercise
  1. If l1,m1,n1 and l2,m2,n2 are the direction cosines of two mutually per...

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  2. Find the angle between the lines whose direction ratios are a,b,c and ...

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  3. Find the equation of a line parallel to x-axis and passing through the...

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  4. If the coordinates of the points A,B,C,D be (1,2,3),(4,5,7),(-4,3,-6) ...

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  5. If the lines (x-1)/(-3) =(y-2)/(2k) =(z-3)/2 and (x-1)/(3k)=(y-1)/1=(z...

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  6. Find the vector equation of the line passing through (1,2,3) and perpe...

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  7. Find the equation of the plane passing through (a,b,c) are parallel to...

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  8. Find the shortest distance between the lines vecr=6hati+2hatj+2hatk+la...

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  9. Find the coordinates of the point where the line through (5,1,6) and (...

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  10. Find the coordinates of the point where the line through (5,1,6) and (...

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  11. Find the coordinates of the point where the line through (3,-4,-5) and...

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  12. Find the vector and cartesian equations of the plane passing through t...

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  13. If the points (1,1,p) and (-3,0,1) are equidistant from the plane vecr...

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  14. Find the equation of the plane passing through the line of intersectio...

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  15. If O is the origin and the coordinates of P be (1,2,-3) , then find th...

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  16. Find the equation of the plane which contains the line of intersection...

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  17. Find the angle between the line vecr=(2hati+2hatj+hatk)+lambda(2hati-3...

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  18. Find the vector equation of the line passing through (1,2,3) and paral...

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  19. If a,b , c are distinct +ve real numbers and a^(2)+b^(2)+c^(2)=1" then...

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  20. The planes 2x -y+4z=5 and 5x-2.5y+10z=6 are

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