What is the correct intuitive explanation for why the dot product of a vector with itself, denoted as ⃗⋅⃗v ⋅ v , does not yield the length of the vector?
A) The dot product is a measure of how much one vector projects onto another, and when a vector is projected onto itself, it accounts for its entire length.
B) The dot product involves the cosine of the angle between vectors, and when applied to a vector and its copy, the cosine of 0 degrees results in 1, not the length of the vector.
C) The dot product considers both the magnitude and direction of vectors, and when applied to a vector and itself, it emphasizes the direction, not just the length.
D) The dot product is a scalar quantity, and when computed for a vector and its copy, it represents a scaling factor rather than the actual length of the vector.
