Question

Sejam os vetores u=(1,1,0), v=(2,0,1) w1=3u-2v, w2=u+3v w3=(1,1,-2). Determinar o volume do paralelepípedo definido pelos vetores w1, w2 e w3.

Answer 1

w1=3(u)-2(v)
w1=3(1,1,0)-2(2,0,1)
w1=(3,3,0)-(4,0,2)
w1=(-1,3,-2)

w2=u+3(v)
w2=(1,1,0)+3(2,0,1)
w2=(1,1,0)+(6,0,3)
w2=(7,3,1)

w3=i+j-2k
w3=(1,1,-2)

Volume do paralelepipedo é definido por w1, w2 e w3, então temos que:

volume do paralelepipedo = |(w1,w2,w3)|, portanto:

$\left[\begin{array}{ccc}-1&3&-2\\7&1&3\\1&1&-2\end{array}\right]$

volume do paralelepipedo = |44|, portanto Vp=44u.v