component of a vector $\mathbf a$ onto vector $\mathbf b$ Just a bit unsure about the definition. When I look online and at other questions on this site it says that the component of $\mathbf a$ onto $\mathbf b$ is $\dfrac{\mathbf a\cdot\mathbf b}{|\mathbf b|}$ but when I look in my notes and at my lecture slides it says that the component of $\mathbf a$ onto $\mathbf b$ is $\dfrac{\mathbf a\cdot\mathbf b}{\mathbf b\cdot\mathbf b}$. Also is the projection of $\mathbf a$ onto $\mathbf b$:
$$\frac{\mathbf a\cdot\mathbf b}{\mathbf b\cdot\mathbf b}\mathbf b?$$

The component -- better the coordinate -- of $a$ in respect to $b\neq0$ is $ab/|b|$.  Since $|b|=\sqrt{bb}$ either your lecture book is wrong or you've made a typo.  The orthogonal projection of $a$ onto $b$ is indeed $\dfrac{ab}{|b|}\dfrac{b}{|b|}=\dfrac{ab}{bb}b$. 
