Let line L1 pass through P1 and have nonzero vector v1 along the line; let line L2 pass th...

Let line L1 pass through P1 and have nonzero vector v1 along the line; let line L2 pass through P2 and have nonzero vector v2 along the line. Let u = Use geometric reasoning for the following:

a) Show that L1 and L2 coincide precisely when u × v1 = 0 and v1 × v2 = 0.

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b) Show that L1 and L2 are parallel and noncoincident precisely when u × v1 ≠ 0 and v1 × v2 = 0.

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c) Show that L1 and L2 intersect at one point precisely when u • v1 × v2 = 0 and v1 v2 ≠ 0.

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d) Show that L1 and L2 are skewed precisely when u • v1 × v2 ≠ 0. Show that in this case the shortest distance between two points on L1, L2 is