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Scalar resolute - Wikipedia, the free encyclopedia

Scalar resolute

From Wikipedia, the free encyclopedia

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.

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