The dot product and the angle between two vectors

The [i]dot product[/i] of vectors [math]\mathbf{u} = \langle u_1, u_2, u_3\rangle [/math] and [math]\mathbf{v} = \langle v_1, v_2, v_3\rangle[/math] is the scalar [math]\mathbf{u}\cdot \mathbf{v} =u_1 v_1 + u_2 v_2 + u_3 v_3 [/math]. The angle between vectors [math]\mathbf{u}[/math] and [math]\mathbf{v}[/math] can be computed using their dot product. The dot product is sometimes called the [i]inner product[/i] or [i]scalar product[/i], because the product results in a scalar, not a vector.[br][br]Use this interactive figure to help you find the angle between two vectors. You can drag points to change the vectors [math]\mathbf{u}[/math] and [math]\mathbf{v}[/math]. Notice that when you hover over a point, arrows appear showing you how the point will move. Click on the point without dragging to change how the point moves.[br]

Information: The dot product and the angle between two vectors