Select the correct statements pertaining to the dot product. \( \square \) The dot product vector is the diagonal in a parallelogram formed by the two vectors \( \vec{u} \) and \( \vec{v} \). \( \square \) The dot product of two vectors is always a scalar. \( \square \) The dot product of orthogonal vectors is always 0 . \( \square \) The dot product of orthogonal vectors is always 1 .

The dot product of two vectors is indeed always a scalar. This means that no matter how many dimensions your vectors span, multiplying them using the dot product will yield a single number, making it quite handy for various calculations in physics and engineering. Additionally, the dot product of orthogonal vectors is always 0. Orthogonal vectors, by definition, are perpendicular to each other, which results in their dot product summing to zero. This property is immensely useful when resolving components in vector analysis or in projections!