Question

Los componentes de u,v,w son u =(1,2,3), v=(2,5,-4), w= (1,1,3)

Answer 1

Dadas las componentes de los vectores u, v y w, se obtiene:

a) (u×v)×w  = (29, -70, -33)

b) u×(v×w)   = (27, -60, -28)

Explicación paso a paso:

Datos;

u=(1,2,3)

v=(2,5,-4)

w=(1,1,3)

a) (u×v)×w

Aplicar producto vectorial o cruz;

$uxv=\left[\begin{array}{ccc}i&j&k\\1&2&3\\2&5&-4\end{array}\right]$

u×v = i[(2)(-4)-(5)(3)]-j[(1)(-4)-(2)(3)]+k[(1)(5)-(2)(2)]

u×v = (-23i +10j +k)

u×v = (-23, 10, 1)

Aplicar producto vectorial o cruz;

$uxvxw=\left[\begin{array}{ccc}i&j&k\\-23&10&1\\1&1&3\end{array}\right]$

(u×v)×w  = i[(10)(3)-(1)(1)]-j[(-23)(3)-(1)(1)]+k[(-23)(1)-(1)(10)]

(u×v)×w  = (29i-70j-33k)

(u×v)×w  = (29, -70, -33)

b) u×(v×w)

Aplicar producto vectorial o cruz;

$vxw=\left[\begin{array}{ccc}i&j&k\\2&5&-4\\1&1&3\end{array}\right]$

v×w = i[(5)(3)-(1)(-4)]-j[(2)(3)-(1)(-4)]+k[(2)(1)-(1)(5)]

v×w = (19i +10j -3k)

v×w = (19, 10, -3)

Aplicar producto vectorial o cruz;

$uxvxw=\left[\begin{array}{ccc}i&j&k\\1&2&3\\19&10&-3\end{array}\right]$

u×(v×w)  = i[(2)(-3)-(10)(3)]-j[(1)(-3)-(19)(3)]+k[(1)(10)-(19)(2)]

u×(v×w)    = (-36i+60j-28k)

u×(v×w)   = (27, -60, -28)