Scalar resolute

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Diagram of the scalar projection in two dimensions.
Diagram of the scalar projection in two dimensions.

The scalar resolute (also known as the scalar projection) of a vector \mathbf{b} in the direction of a vector \mathbf{a} (also "\mathbf{b} on \mathbf{a}"), is given by:

\mathbf{b}\cdot\mathbf{\hat a} = |\mathbf{b}|\cos\theta

where θ is the angle between the vectors \mathbf{a} and \mathbf{b} and \hat{\mathbf{a}} is the unit vector in the direction of \mathbf{a}.

The scalar resolute is a scalar, and is the length of the orthogonal projection of the vector \mathbf{b} onto the vector \mathbf{a}.

Multiplying the scalar resolute by \mathbf{\hat a} converts it into the vector resolute, a vector.

[edit] See also

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