MathAlgebraLinear algebraVectors and vector spaces

Vector dot product

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What is the algebraic expansion of $\vec{u} \cdot \vec{v}$ if they are both vectors in $\mathbb{R}^3$ ?

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\left[ u_x \cdot v_x, u_y \cdot v_y, u_z \cdot v_z \right]

u_x \cdot v_x + u_y \cdot v_y + u_z \cdot v_z

u_x + v_x \cdot u_y + v_y \cdot u_z + v_z

u_x \cdot (v_x + v_y + v_z) + u_y \cdot (v_x + v_y + v_z) + u_z \cdot (v_x + v_y + v_z)

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