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Let $ u$, $v$ and $ w$ be vectors in R3 such that $u* v = (1, 0,-1)$ and $w *u = (-1,0, 0).$ Find the area of the parallelogram defined by $u$ and $(v+w)$.

So my thought was: $u*(v+w) = u*v + u*w$. I know that the parallelogram defined by $uāˆ—v$ has area $\sqrt2$ but I can't find the area of the other one. Any help on this?

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    you have $u*v$ and $w*u$ what more do you need? ā€“ 2017-01-22

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You have $u*v$ and $w*u$. Remember that $u*w=-w*u$.

Now, calculate the vector:

$$u*v-w*u=(1,0,-1)-(-1,0,0)=(2,0,-1)$$

The area will bee then

$$|(2,0,-1)|=\sqrt{5}$$

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    Ok, did not know that. But the area of $-(w*u)$ is the same as $u*w$, right? So how is the answer $\sqrt5$? ā€“ 2017-01-22