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I tutor a calculus-based general physics course in kinematics, and similar topics, and, I recently had a student approach me about his inability to grasp the scalar/dot product, in vector operations. His concerns seemed to convey that he was having trouble "visualizing" a dot product, comprehending real-to-life situations where it would be applicable and, understanding why the formula relating the dot product of two vectors always involved the

**of the angle between them.**

*cosine*I've heard it explained before, in loose terms, that one could look at the result of a scalar/dot product as an area, and the result of the vector/cross product as a volume. I'm hesitant to endorse that representation because, I fail to see the accuracy of the comparison.

So, if any of you viewers can offer, what you feel to be, an effective example problem or explanation, from either an experience teaching or enduring the presentation of similar subject matter, it would be greatly appreciated. Thank You All!!