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Find the shortest distance between the lines `vecr =(8+3lambda) hati - (9 +16lambda) hatj+(10+7lambda)hatk` and `vecr= (15hati + 29hatj + 5hatk) + mu(3hati + 8hatj - 5hatk ).`

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Find the shortest distance between the lines l_1 and l_2 whose vector equations are vecr=hati+hatj+lambda(2hati-hatj+hatk) and vecr=2hati+hatj-hatk+mu(3hati-5hatj+2hatk).

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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
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  3. Find the shortest distance between the lines vecr =(8+3lambda) hati - ...

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  6. Find the shortest distance between the lines vecr=(lambda-1)hati+(...

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  8. Find the vector equation of a plane which is at a distance 11 units fr...

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  10. Find the cartesian equation of the plane through the point (2,-1, 1) a...

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  11. Find the vector equation of the plane passing through the points (1, -...

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  13. A plane meets the co-ordinate axes at A, B and C such that the centroi...

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  14. Show that the plane through (1, 1, 1), (1,-1, 1) and (-7, 3, -5) is pe...

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  15. The foot of perpendicular from the origin to the plane is (4, -2, -5) ...

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  16. Find the equation of the plane passing through the point (-1,2, 1) and...

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  17. Find the equation of the plane containing the line of intersection of ...

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

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  20. Find the cartesian equation of the plane| through the intersection of ...

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