The following applet shows
1. The inner product(which is a scale) is defined as \vec{A}\cdot\vec{B}=|\vec{A}|\,|\vec{B}|\cos\theta ,
  So projection of vector \vec{A} into another direction \vec{B} can be calculated as \vec{C}=(\vec{A}\cdot \hat{B}) \hat{B}=(\vec{A}\cdot\frac{\vec{B}}{|\vec{B}|})\frac{\vec{B}}{|\vec{B}|}

2. The cross product \vec{D}=\vec{A}\times\vec{B}, |\vec{D}|=|\vec{A}|\, |\vec{B}| \sin\theta where \theta is the angle between \vec{A} and \vec{B}

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