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The orthogonal projection of $y$ onto the line spanned by a nonzero vector $v$ is given by the formula $\frac{y \cdot v}{v \cdot v} v$. This formula scales the vector $v$ by the ratio of the dot product of $y$ and $v$ to the dot product of $v$ with itself.

Conditions: The vector $v$ must be nonzero.; The projection is onto the line spanned by $v$.

The orthogonal projection of $y$ onto the line spanned by a nonzero vector $v$ is given by the formula $\frac{y \cdot v}{v \cdot v} v$. This formula scales the vector $v$ by the ratio of the dot product of $y$ and $v$ to the dot product of $v$ with itself.

Conditions: The vector $v$ must be nonzero.; The projection is onto the line spanned by $v$.