Final answer:
Direction angles inform us about the direction of the vector. They do not provide information on the magnitude, scalar product, or vector's cross product of a given vector.
Step-by-step explanation:
Knowing the direction angles of a vector helps us understand the direction of the vector. The direction angles correspond to angles made by the vector with the positive direction on each of the coordinate axes, usually in a three-dimensional space. However, the direction angles themselves do not directly give us information about the magnitude of the vector, scalar product, or vector's cross product.
The magnitude of a vector can be found by using the scalar components (e.g., Ax, Ay, and if in three dimensions, Az) and applying the Pythagorean theorem. The scalar product (dot product) is calculated using the magnitudes of two vectors and the cosine of the angle between them, while the vector product (cross product) involves the magnitudes of two vectors and the sine of the angle between them, resulting in a vector that is perpendicular to both.
To answer the question, knowing the direction angles of a vector primarily gives us the B) Direction of the vector, as these angles are the angles made by the vector with respect to the coordinate axes.