Can the resultant of two vectors be zero? If so, under what conditions? Explain your answer.
Answer (1)
Yes, the resultant of two vectors can be zero. This happens under certain conditions:
Magnitude: The two vectors must have the same magnitude. This means their lengths, or the amounts of the force or quantity they represent, are equal.
Direction: The vectors must be in directly opposite directions. This means if one vector points in a specific direction, the other one should point exactly in the opposite direction.
When these two conditions are met, the forces or quantities that the vectors represent cancel each other out, resulting in a net force of zero.
For example, imagine two people playing tug-of-war. If both pull with a force of 50 Newtons, but in opposite directions, the rope will not move because the forces balance each other out:
F 1 = − F 2
Where F 1 and F 2 are the two vectors.
This principle is not only limited to physical forces but can also apply to other scenarios involving vectors, such as balancing concurrent financial gains and losses, or balancing probabilities in statistics.
Understanding this concept is important as it explains phenomena of equilibrium and balance in physics and engineering.
