Problem Set 4, Due Fifth Class Meeting
(1) Find the volume of the parallelopiped generated by the vectors
<1,2,3>,<5,9,11 >and <2,3,5>.
(2) Show that the volume of a parallelopiped generated by
< a, b, c >,< r, s, t > and < x, y, z > is given by
det
a b c
x y z
r s t
.
(3) The algebraic definition of right handed. We say that an ordered triple of
vectors (< a, b, c >, < x, y, z >, < r, s, t >) is right handed if Show that
det
a b c
x y z
r s t
>0.
Show that (< a, b, c >, < x, y, z >, < a, b, c > ×< x, y , z >) is right-handed
so long as the cross-product is not equal to ~
0.
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