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Find the shortest distance (S.D.) betwee...

Find the shortest distance (S.D.) between the lines : `vec r = hat i + hat j + lambda (2 hat i- hat j + hat k)` and `vec r = 2 hat i + hat j- hat k + mu (3 hat i - 5 hat j + 2 hat k)`.

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Find the shortest distance between the lines vec r = (hat i + 2 hat j + hat k) + lambda (hat i - hat j + hat k) and vec r = ( 2 hat i - hat j - hat k) + mu ( 2 hat i + hat J + 2 hat k)

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Find the shortest distance between the lines vec r = 6 hat i + 2 hat j + 2 hat k) lambda (hat i - 2 hat j + 2 hat k ) and vec r = - 4 hat i - hat k + mu (3 hat i - 2 hat j - 2 hat k)

Find the shortest distance between the lines vec r = 2 hat i + 3 hat j + hat k + lambda (2 hat i - hat j + 3 hat k ) and vec r = 7 hat i + 5 hat j + 6 hat k + mu ( hat i + 3 hat j + 5 hat k )

Find the shortest distance between the lines vec , = 2 hat i + 3 hat J + 4 hat k + lambda ( 2 hat i - hat J + hat k) and vec r = 3 hat i - 2 hat j- hat k + mu (3 hat i + 2 hat j- 4 hat k).

Find the shortest distance between the lines vec r = hat i + 2 hat j + 3 hat k ) + lambda (hat i- 3 hat j + 2 hat k) and vec r = ( 4 hat i + 5 hat j + 6 hat k ) + mu ( 2 hat i + 3 hat j + hat k )

Find the shortest distance between lines vec r=( hat i+2 hat j+ hat k)+lambda(2 hat i+ hat j+2 hat k) and vec r=2 hat i- hat j- hat k+mu(2 hat i+ hat j+2 hat k)dot

Find the shortest distance between the lines vec r=(4 hat i- hat j)+lambda( hat i+2 hat j-3 hat k)a n d vec r=( hat i- hat j+2 hat k)+mu(2 hat i+4 hat j-5 hat k)dot .

Find the shortest distance between the lines given by the equations vec r= hat i + 2 hat j - 3 hat k + lambda (3 hat I - 4 hat j - hat k) , vec r= 2 hat i - hat j + hat k + mu (hat i - hat j -5 hat k) .

Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+lambda( hat i- hat j+ hat k) and the plane vec r = dot(2 hat i- hat j+ hat k)=4.

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