Question

Consider the following triple of vectors:?
Consider the following triple of vectors:
u = [4,3,1], v = [1,5,5], w = [-4,-1,-5].

What is the volume of the parallelopiped having u, v and w as edges?

Answer 1

volume can be determined by ..... ugh, just read this somewheres

Answer 2

the determinant of the associated column matrix

Answer 3

\[det.of:\begin{pmatrix}4&1&-4\\3&5&-1\\1&5&-5\end{pmatrix}\]

Answer 4

4(-25-(-5))
-3(-5-(-20))
+1(-1-(-20))

4(-25+5) = 4(-20) = -80
-3(-5+20) = -3(15) = -45
+1(-1+20) = +1(19) = +19
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volume

if i kept the math straight that is

Answer 5

and if it goes negative just strip the sign away and its all good