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

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The correct Answer is:
`=9`
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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) .

Find the shortest distance between the lines vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

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 lines l_1 and l_2 given by vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(2hati+3hatj+6hatk) .

Find the angle between the following pairs of lines : (i) vecr=2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and veck=7hati-6hatk+mu(hati+2hatj+2hatk) (ii) vecr=3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

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).

Find the shortest distance between the lines vecr=(lambda-1)hati+(lambda+1)hatj-(1+lambda)hatk and (vecr=(1-mu)hati+(2mu-1)hatj+(mu+2)hatk .

Find the vector equation of the plane containing the lines vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) .

Find the angle between the lines vecr = (3 + lambda)hati + 2(1 + lambda)hatj + 2(1 – 2lambda)hatk and vecr=5hatj-2hatk+mu(3hati+2hatj-6hatk).

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE-11
  1. Find the equation of a line parallel to X- axis and passing through th...

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

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

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

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

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

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

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

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

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

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  11. If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane v...

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

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

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

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  15. Find the distance of the point (-1, -5, -10) from the point of interse...

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

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  17. Find the vector equation of the line passing through the point (1, 2, ...

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  18. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  19. Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = ...

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

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