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(of a vector on a vector)

Given non-zero vectors **a** and **b**, let and be directed line-segments representing **a** and **b**, and let *θ* be the angle between them (*θ* in radians, with 0≤*θ*≤*π*). Let *C* be the projection of *B* on the line *OA*. The vector projection of **b** on **a** is the vector represented by Since |*OC*|=|*OB*|cos*θ*, this vector projection is equal to |**b**|cos*θ* times the unit vector **a**/|**a**|. Thus the vector projection of **b** on **a** equalsThe scalar projection of **b** on **a** is equal to (**a**. **b**)/|**a**|, which equals |**b**|cos*θ*. It is positive when the vector projection of **b** on **a** is in the same direction as **a**, and negative when the vector projection is in the opposite direction to **a**; its absolute value gives the length of the vector projection of **b** on **a**.

*Subjects:*
Mathematics.

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