(au) × v + (bu) × v = [(a + b)u] × v
u = ( x , y , z )
v = ( x₂, y₂,z₂)
LHS:
= (au) × v + (bu) × v
= [ ay z₂- y₂az , - (axz₂- x₂az) , axy₂- x₂ay ] + [ by z₂- y₂bz , - (bxz₂- x₂bz) , bxy₂- x₂by ]
RHS:
= [(a + b)u] × v
= [ (a + b)x , (a + b)y , (a + b)z ] × ( x₂, y₂,z₂)
= [ (a + b)y z₂- y₂(a + b)z , -((a + b)x z₂- x₂(a + b)z) , (a + b)x y₂- x₂(a + b)y]
This is how far I got to prove left side equals right side. . .now I don't know what to do.