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

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

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

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by: vec(r) = (3 hat(i) + 8 hat(j) + 3 hat(k) ) + lambda (3 hat(i) - hat(j) + hat(k)) and vec(r) = (-3 hat(i) - 7 hat(j) + 6 hat(k)) + mu (-3 hat(i) + 2 hat(j) + 4 hat(k)) .

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

Show that the lines vec(r) =(hat(i) +2hat(j) +hat(k)) +lambda (hat(i)-hat(j)+hat(k)) " and " vec(r ) =(hat(i) +hat(j) -hat(k)) + mu (hat(i)- hat(j) + 2hat(k)) Do not intersect .

vec(r ) =(6hat(i) +3hat(k) ) + lambda(2hat(i) -hat(j) +4hat(k)) vec(r )=(-9hat(i) +hat(j) -10hat(k)) + mu (4hat(i) +hat(j) +6hat(k))

vec(r )=(hat(i) +hat(j)) +lambda(2hat(i) -hat(j) +hat(k)) vec(r )=(2hat(i) +hat(j) -hat(k)) + mu (3hat(i) -5hat(j) +2hat(k))

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by r=(3hat(i)+8hat(j)+3hat(k))+lambda(3hat(i)-hat(j)+hat(k)) and r=(-3hat(i)-7hat(j)+6hat(k))+mu(-3hat(i)+2hat(j)+4hat(k)) .

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

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