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What's the difference?

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>Isn't the direction vector just the cross-product of the two normal vectors of the planes?

You're right.

I don't think it's that strange that you would have the same answer to both questions.
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Could it be that they want you to find a direction vector using a different technique? For example, solving a system of equations.

Or perhaps, by "*the* direction vector", they mean the (appropriately oriented) unit vector in that direction?
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Unit length?

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