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Find the shortest distance between the l...

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))`

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

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

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

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