Final answer:
Two vectors with equal magnitudes and opposite directions will sum to zero, forming the vector equivalent of null displacement. The concepts of vector addition, equilibrant vectors, and antiparallel vectors describe this phenomenon where each vector's effect is negated by the other, resulting in a resultant vector of zero magnitude.
Step-by-step explanation:
If two vectors have equal magnitudes and are opposite in direction, their sum is indeed zero. This scenario is possible because the sum of two vectors follows the principles of vector addition, which is both commutative and associative. The resultant vector, in this case, has a magnitude of zero because each vector cancels out the effect of the other. Imagine walking in one direction and then walking back the same path with the same number of steps; you would end up at the starting point, which confirms that the displacement is zero - a real-world analogy of this vector situation.
The concept of the equilibrant vector is applicable here. By definition, the equilibrant has the same magnitude as the resultant vector but in the opposite direction, meaning it cancels the resultant when the two are added. If you were to add a vector to its equilibrant, the total would be a zero vector, as they are equal in size but opposite in direction, which meets the criteria of the original question.
Furthermore, if we examine the subtraction of two vectors, A and B, which are equal in magnitude and opposite in direction, the result A - B would have the same direction as vector A. This is because subtracting B effectively adds the opposite of B to A, which means doubling A in the direction in which it points.
To generalize the concept, vectors can be multiplied by scalars to change their magnitude, keeping the direction intact if the scalar is positive, or reversing it if the scalar is negative. Antiparallel vectors are those that are parallel but have opposite directions – a condition fulfilled by the vectors in question. A pair of antiparallel vectors having equal magnitudes sum up to a zero vector.