Given the three non-coplanar vectors a, b, c, and defining v = a b c,

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Given the three non-coplanar vectors a, b, c, and defining v = a · b × c, three further vectors are defined as

a' = bxclv b' = cx alv c = a  blv

Show that

where v' = a' b' X c' Deduce that a a' = b.b' = c.c' = 1 a.b' = a.c' = b.a' = b.c' = c.a' = c.b' = 0

If a vector is written in terms of a, b, c as

r = aa + b + yc

evaluate α, β, γ in terms of a´, b´ and c´.

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