# What's the math behind Vector multiplication?

Can someone explain to me why a cylinder with this node tree becomes a double-sided cone?

I have tried to check it and to calculate it by hand using a vector $$(3,0,0)$$ but can't figure it out. The green dotted line is supposed to represent the side of the cylinder befor the math operation. Somehow the vector $$(3,0,0)$$ must become the vector $$(0,0,0)$$.

In the node tree, the separate xyz node takes the $$z$$ value and makes it the $$x$$ and $$y$$ value of the new vector, while $$z$$ is defined as $$1$$.

Then the vectors are multiplied with each other. I am not a mathematician but according to chatGPT the cross product can be used to calculate this. obviously $$(-3,-3,3)$$ is the result. But it must be $$(0,0,0)$$.

• That position node is a field node, and will not reference the object location, but instead the position of each point as it is processed through the tree. Feb 2, 2023 at 21:45
• Oh I misunderstood your test case Feb 2, 2023 at 21:50
• Cross product is different, vector multiply is multiplication straight across, so the result here is 0,0,0 Feb 2, 2023 at 21:53
• You're multiplying the position vectors of all your points by 1 on the Z, so their height does not change. But you're multiplying their horizontal placement (X and Y values) by their heights. The ones on the upper part just get bigger since they're being multiplied by a positive number, but the ones on the lower part "flip" (all the while getting bigger) since they're being multiplied by a negative number (their Z is below 0). Since the bottom "flips" but the top stays fixed, it twists, creating this cone shape. Feb 2, 2023 at 21:57
• Here's a demonstration of what's happening: i.imgur.com/Ewp7DX6.mp4 Feb 2, 2023 at 22:12

First - I would strongly recommend against using ChatGPT as a general knowledge engine. It has frequently been shown to provide confident, totally incorrect answers. For instance, the cross product of $$(3,0,0)$$ and $$(0,0,1)$$ is $$(0,-3,0)$$, not $$(-3,-3,3)$$

Second, you're using element-wise multiplication: for vertices on the center circle of your cylinder $$(z=0)$$ and your current node setup, you're performing

$$(x,y,z) * (z, z, 1) = (xz, yz, z) = (0, 0, 0)$$

Change your vector math node to "Cross Product" and you should be in business.

• @quellenform Careful, ChatGPT will come for you one day :)
– Neil
Mar 17, 2023 at 13:45
• @Neil Seriously, I prefer to learn and know things myself rather than depend on an AI. Therefore: Rather no, because the day will come when real knowledge counts, completely independent of an assisting mechanism ;-) Mar 17, 2023 at 13:49
• @quellenform I agree with you, we definitely need to avoid reliance on AI, but I'm certain it's going to be a valuable tool for us in many ways.
– Neil
Mar 17, 2023 at 13:57