Vector Projection
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High Quality Content by WIKIPEDIA articles! The vector resolute (also known as the vector projection) of two vectors, mathbf{a} in the direction of mathbf{b} (also "mathbf{a} on mathbf{b}"), is given by: (mathbf{a}cdotmathbf{hat b})mathbf{hat b}text{ or }( mathbf{a} costheta)mathbf{hat b} where is the angle between the vectors mathbf{b} and mathbf{a}; the operator cdot is the dot product; and hat{mathbf{b}} is the unit vector in the direction of mathbf{b}. The vector resolute is a vector, and is the orthogonal projection of the vector mathbf{a} onto the vector mathbf{b}. The vector resolute is...
High Quality Content by WIKIPEDIA articles! The vector resolute (also known as the vector projection) of two vectors, mathbf{a} in the direction of mathbf{b} (also "mathbf{a} on mathbf{b}"), is given by: (mathbf{a}cdotmathbf{hat b})mathbf{hat b}text{ or }( mathbf{a} costheta)mathbf{hat b} where is the angle between the vectors mathbf{b} and mathbf{a}; the operator cdot is the dot product; and hat{mathbf{b}} is the unit vector in the direction of mathbf{b}. The vector resolute is a vector, and is the orthogonal projection of the vector mathbf{a} onto the vector mathbf{b}. The vector resolute is also said to be a component of vector mathbf{a} in the direction of vector mathbf{b}. The other component of mathbf{a} (perpendicular to mathbf{b}) is given by: mathbf{a} - (mathbf{a}cdotmathbf{hat b})mathbf{hat b}. (By triangle addition of vectors.) The vector resolute is also the scalar resolute multiplied by mathbf{hat b} (in order to convert it into a vector, or give it direction).e.g. in this case scalar resolute is (mathbf{a}cdotmathbf{hat b}).
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