Scalar resolute

Scalar resolute

The scalar resolute, also known as the scalar projection or scalar component, of a vector mathbf{b} in the direction of a vector mathbf{a} is given by:

:mathbf{b}cdotmathbf{hat a} = |mathbf{b}|cos heta

where heta 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}. This is also known as "mathbf{b} on mathbf{a}".

For an intuitive understanding of this formula, recall from trigonometry that cos heta = frac and simply rearrange the terms by multiplying both sides by |mathbf{b}|.

The scalar resolute is a scalar, and is the length of the orthogonal projection of the vector mathbf{b} onto the vector mathbf{a}, with a minus sign if the direction is opposite.

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

ee also

* vector resolute
* scalar product
* cross product


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