Helena has saved $595 to put toward snowboarding equipment and lift tickets at the hill. Each lift ticket costs $35. If she want
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Recall that for 3 vectors , all in
, the vector triple product
So
Also recall the scalar triple product,
which gives the signed volume of the parallelipiped generated by the three vectors . When either
or
, the parallelipepid is degenerate and has 0 volume, so
and the above reduces to
so that
The scalar triple product has the following property:
Since is a scalar, we can factor it out to get
and by the property above we have
and so we end up with
as required.