given the vectors u x1 y1 z1 v x2 y2 z2 and w x3 y3 z3 Sh

given the vectors u = (x1, y1, z1), v = (x2, y2, z2) and w = (x3, y3, z3). Show that u (v x w) = (u x v) .w ?

u = x₁, y₁, z₁,
v = x₂, y₂, z₂ ,
w = x₃, y₃, z₃
(vxw)=(y₂z₃-y₃z₂),(x₃z₂-x₂z₃),(x₂y₃-x₃y₂)
(uxv)=(y₁z₂-y₂z₁),(x₂z₁-x₁z₂),(x₁y₂-x₂y₁)

u.(vxw)= x₁, y₁, z₁.(y₂z₃-y₃z₂),(x₃z₂-x₂z₃),(x₂y₃-x₃y₂) =x₁(y₂z₃-y₃z₂)+ y₁(x₃z₂-x₂z₃) +z₁(x₂y₃-x₃y₂)
u.(vxw)=x₁y₂z₃-x₁y₃z₂+ x₃y₁z₂-x₂y₁z₃ +x₂y₃z₁-x₃y₂z₁

(uxv).w=(y₁z₂-y₂z₁),(x₂z₁-x₁z₂),(x₁y₂-x₂y₁)x₃, y₃, z₃
(uxv).w=(y₁z₂-y₂z₁)x₃+(x₂z₁-x₁z₂)y₃+(x₁y₂-x₂y₁)z₃
(uxv).w=x₃y₁z₂-x₃y₂z₁+x₂y₃z₁-x₁y₃z₂+x₁y₂z₃-x₂y₁z₃
(uxv).w=x₁y₂z₃-x₁y₃z₂+ x₃y₁z₂-x₂y₁z₃ +x₂y₃z₁-x₃y₂z₁

so u (v x w) = (u x v) .w

given the vectors u = (x1, y1, z1), v = (x2, y2, z2) and w = (x3, y3, z3). Show that u (v x w) = (u x v) .w ?Solutionu = x1, y1, z1, v = x2, y2, z2 , w = x3, y3

given the vectors u x1 y1 z1 v x2 y2 z2 and w x3 y3 z3 Sh

Solution

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