A vector can, most definitely, be resolved into its constituent component vectors. Hence the given statement is false.
A vector quantity has both a direction and a magnitude. Vector components are used to break down a vector into two scalar components. Correspondingly, the component vectors should be capable of giving us both the magnitude and the direction of the vector, that is the vector itself.
The most common example of resolving the vector into its components is faced in the motion of an object over an incline. The weight of the object acts downwards due to earth's gravity. However, it also has to be divided into two components: along the incline and perpendicular to the inclined surface. Given the angle of incline, the weight can be resolved into the two component vectors and can be used to solve the numericals.
Hope this helps.