#What is the application/importance of dot product in vectors?

11 messages · Page 1 of 1 (latest)

waxen adder
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Hello, sorry to disturb you all, I understood how dot product on vectors work, I mean how they are calculated, like we take the summation of each pair of x1 * y1 until xn * y2 (Please confirm if this is correct :c). But I was wondering, why is it important to know/do that? For example in real-life applications where is that useful, what does it allow us to do?

What does it allows us to see/visualize in a vector space?

olive oreBOT
ember shore
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To my knowlege the dot product shows the relation of two vectors to each other.
Example would be that if the dot product is zero then the angle between the two vectors is 90 degrees

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Visually it means to project one vector on the other

hybrid anchor
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,, x \cdot y = $ \sum_{i=1}^{n} x_i y_i

shrewd pivotBOT
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pola_touche
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hybrid anchor
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But the more geometrical interpretation is the following

waxen adder
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oh I see

waxen adder
# hybrid anchor

so basically, it's important so that we know how two vectors are arranged in space? Like the angle in-between them ?