The answer to this can of course be described mathematically. However, here I want to describe why conceptually. The dot product of two vectors is the overlap of the two vectors or the shadow of one on the other vector. If two vectors are perpendicular or at a right angle to each other then they have no overlap or shadow onto each other.
thank of a vector pointing straight up and a vector pointing straight to the right where both of them start at the origin. The vector pointing up doesn’t have any length or overlap to the right. Think of the vector pointing to the right. It has no length upwards either. It’s dot product is thus zero.
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