Explanation

The correct answer is B) Vector product (also known as cross product).

Why this is correct:

1. Vector product (cross product) of two vectors produces a third vector that is perpendicular to both original vectors.
2. In a 3D coordinate system, if you have orthogonal unit vectors for X and Y axes, the cross product of X × Y gives you the Z axis vector.
3. This follows the right-hand rule convention for coordinate systems.

Why other options are incorrect:

• A) Scalar product: Produces a scalar value, not a vector.
• C) Normalization: Converts a vector to unit length but doesn't change its direction.
• D) Translation: Moves points or vectors in space but doesn't create perpendicular vectors.
• E) Projection: Finds the component of one vector along another vector's direction.

Mathematical Context:

In linear algebra and 3D geometry, the cross product is specifically designed to find a vector perpendicular to two given vectors. For orthogonal unit vectors $\hat{i}$ (X-axis) and $\hat{j}$ (Y-axis), $\hat{i} \times \hat{j} = \hat{k}$ (Z-axis).