- #1

Macleef

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## Homework Statement

Prove:

(au) × v + (bu) × v = [(a + b)u] × v

## Homework Equations

http://en.wikipedia.org/wiki/Cross_product

## The Attempt at a Solution

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.

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