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

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

Find the shortest distance between two lines whose vector equations are : vecr=hati-7hatj-2hatk+lambda(hati+3hatj+2hatk) and vecr=-3hati+4hatj-2hatk+mu(-hati+2hatj+hatk)

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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 shortest distance between two lines whose vector equations are : vecr=hati+2hatj+hatk+lambda(hati+hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)

Find the shortest distance between the following lines whose vector equations are : vecr=3hati-15hatj+9hatk+lambda(2hati-7hatj+5hatk) and vecr=(2mu-1)hati+(1+mu)hatj+(9-3mu)hatk

1 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)

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the vector equation of the line passing through (1, 2, 3) and per...

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  2. Find the equation of the plane passing through (a, b, c) and parallel ...

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  3. Find the shortest distance between the following lines whose vector eq...

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  4. Find the coordinates of the points where the line through (5,1,6) and ...

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

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  6. Find the coordinates of the point where the line through (3, – 4, – 5)...

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  7. Find the equation of the plane passing through the point (-1, 3, 2) an...

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  8. If the points (1, 1, p) and (– 3, 0, 1) be equidistant from the plane ...

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

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  10. If O be the origin and the coordinates of P be (1, 2, – 3), then find ...

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

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  12. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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

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  14. Find the vector equation of the line passing through the point (1,2,-4...

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  15. Prove that if a plane has intercepts a,b,c and is at a distance of p u...

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  16. Find the Distance between the two planes 2x+3y+4z=4 and 4x+6y+8z=12

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

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  18. The x, co-ordinate of a point on the line joining the points Q (2, 2, ...

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  19. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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  20. Find the equation of a plane which is at a distance 3sqrt3 units from ...

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