Understanding Dot Product: Identity and Unit Vectors

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The dot product of a unit vector (e) with a non-unit vector (A) simplifies to the magnitude of vector A multiplied by the cosine of the angle between them. This relationship indicates that the dot product represents the component of vector A in the direction of the unit vector e. Without additional information about the angle or the magnitude of vector A, further simplification is not possible. The discussion highlights that the dot product serves as a measure of projection rather than an identity. Understanding this concept is crucial for applications in physics and engineering.
don_anon25
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What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity?

Thanks,
don_anon25
 
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don_anon25 said:
What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity?

Thanks,
don_anon25

Let a be a unit vector and b be another vector. a * b = |a||b|cosθ. Since a is a unit vector, this becomes a * b = |b|cosθ. I believe that without more information, this is as far as it can be simplified.
 
don_anon25 said:
What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity?

Thanks,
don_anon25

<br /> \hat e\cdot\vec A is the component of \vec A along the \hat e-direction.
 
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