## anonymous 4 years ago 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?

1. amistre64

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

2. amistre64

the determinant of the associated column matrix

3. amistre64

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

4. amistre64

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 ------ volume if i kept the math straight that is

5. amistre64

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