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Compute the shortest distance between...

Compute the shortest distance between the lines
`vec(r )=(hat(i) -hat(j)) + lambda (2hat(i) -hat(k)) " and " vec(r ) =(2hat(i) -hat(j)) + mu (hat(i) - hat(j) -hat(k))`
Determine whether these lines intersect of not.

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Verified by Experts

The correct Answer is:
`SD =(sqrt(14))/(14) ne 0` the given lines do not intersect
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Find the shortest distance between the lines L_(1) " and " L_(2) given by vec( r )=hat(i) +hat(j) +lambda(2hat(i)-hat(j)+hat(k)) " and " vec(r )=2hat(i) +hat(j)-hat(k) +mu (4hat(i) -2hat(j) +2hat(k))

RS AGGARWAL-STRAIGHT LINE IN SPACE-Exercise 27D
  1. Find the shortest distance between the given line vec(r )=(hat(i) +h...

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  2. vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) ...

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  3. vec(r ) =(hat(i) +2hat(j) +3hat(k)) + lambda(hat(i) -3hat(j) +2hat(k))...

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  4. Find the shortest distance between the given line vec(r )=(hat(i) +2h...

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  5. Find the shortest distance between the given line vec(r ) =(hat(i)+2h...

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  6. Find the shortest distance between the given line vec(r ) =(6hat(i) +...

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  7. Find the shortest distance between the given line vec(r) =(3-t) hat(i...

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  8. Find the shortest distance between the given line vec(r ) =(lambda-1)...

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  9. Compute the shortest distance between the lines vec(r )=(hat(i) ...

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  10. Show that the lines vec(r )=(3hat(i) -15hat(j) + 9hat(k)) + lambd...

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  11. Show that the lines vec( r)=(2hat(i) -3hat(k)) + lambda(hat(i) +2h...

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  12. Show that the lines vec(r )=(hat(i) +2hat(j) +3hat(k)) + lambda(2h...

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  13. Find the shortest distance between the lines vecr=(hati+2hatj-4hatk)+...

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  14. Find the distance between the parallel lines L(1) " and " L(2) w...

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  15. Find the vector equtions of a line passing through the point (2,...

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  16. Write the vector equations of each of the following lines and h...

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  17. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/...

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  18. Find the shortest distance distance between the following lines :(x-1)...

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  19. Find the shortest distance between the lines(x-12)/(-9) =(y-1)/(4)=(z-...

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