Question

4 – Dados os vetores u=i+2j+k e v=(-1,4,4), calcule:

a) u×v

b) 2u×3v

c) u×u

d) v×v

Answer 1

u=(1,2,1)

v=(-1,4,4)

a) u x v

$\left[\begin{array}{ccc}i&j&k\\1&2&1\\-1&4&4\end{array}\right]= 4i - 5j + 6k$

b) 2ux3v

2u=(2,4,2)

3v=(-3,12,12)

$\left[\begin{array}{ccc}i&j&k\\2&4&2\\-3&12&12\end{array}\right]= 24i - 30j + 36k$

c) uxu

$\left[\begin{array}{ccc}i&j&k\\1&2&1\\1&2&1\end{array}\right] = 0i + 0j + 0k$

d) vxv

$\left[\begin{array}{ccc}i&j&k\\-1&4&4\\-1&4&4\end{array}\right] = 0i + 0j + 0k$