Final answer:
A vector remains unchanged only when it is translated parallel to itself; rotation, scaling by multiplication, and addition of another vector will all change the original vector.
Step-by-step explanation:
The operation that will not change a vector is to translate it parallel to itself. When a vector is translated, its orientation and magnitude remain unchanged. Translation of a vector means moving it without rotating it or changing its length or direction.
Option a, rotate it, will change the direction of a vector; option c, multiply it by a constant factor, will change the magnitude of the vector if the factor is anything other than one; option d, adding a constant vector to it, will change its magnitude and possibly its direction, resulting in a new resultant vector.
When a vector is multiplied by a positive scalar, the magnitude changes, but the direction stays parallel (unless the scalar is negative, which then flips the direction). Moreover, vector addition is commutative and associative—it results in a combined vector with possibly different magnitude and direction from the original components.