- 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 theunit 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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