Explanation:

The cross product of two vectors is defined as follows:

If a and b are two non-zero vectors, then their cross product, denoted by a × b, is a vector which is perpendicular to both a and b. In other words, it is a vector which is orthogonal to the plane containing a and b.

Now, if the cross product of two non-zero vectors is zero, then it means that the two vectors are perpendicular to each other. However, the question asks us to determine the relationship between the two vectors when their cross product is zero. In other words, we need to determine whether the two vectors are collinear, co-directional, co-initial, or co-terminus.

Collinear Vectors:

Two vectors are said to be collinear if they lie on the same line. In other words, they have the same direction or the opposite direction.

Co-directional Vectors:

Two vectors are said to be co-directional if they have the same direction.

Co-initial Vectors:

Two vectors are said to be co-initial if they have the same initial point.

Co-terminus Vectors:

Two vectors are said to be co-terminus if they have the same terminal point.

Conclusion:

Now, if the cross product of two non-zero vectors is zero, then it means that the two vectors are perpendicular to each other. This implies that they cannot be co-directional or collinear. Also, they need not be co-initial or co-terminus as they can have different initial and terminal points. Therefore, the only possible relationship between the two vectors is that they are collinear. Hence, the correct answer is option A.