Numerical / Calculation-Based

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1.
Find the volume of the parallelepiped with edges a=3i+j+k, b=i+2j+k, c=i+j+3k.
2.
Find the value of lambda for which (1,2,3), (4,1,2), (lambda,-1,1) are coplanar.
3.
Find the shortest distance between lines r=(1,2,3)+t(2,3,4) and r=(2,4,5)+s(3,4,5).
4.
Find the shortest distance between lines r=(1,2,3)+t(2,3,4) and r=(2,4,5)+s(3,4,5).
5.
Find the volume of the parallelepiped with edges a=2i+3j+k, b=i-j+2k, c=i+2j-k.

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