Yes, the resultant of two vectors can be zero under certain conditions. Let’s analyze each option in detail:
Option A: Yes, when the two vectors are the same in magnitude and direction
If two vectors have the same magnitude and same direction, their sum will not be zero. Instead, the resultant vector will be the sum of the two vectors, which will have the same direction and a magnitude equal to the sum of the magnitudes of the two vectors. Therefore, the resultant cannot be zero in this case.
Conclusion for A: Incorrect
Option B: No
This is not correct. As we will see in the next options, the resultant of two vectors can indeed be zero under certain conditions. Therefore, it is not always true that the resultant cannot be zero.
Conclusion for B: Incorrect
Option C: Yes, when the two vectors are the same in magnitude but opposite in sense
If two vectors have the same magnitude but are opposite in direction (opposite sense), they will cancel each other out when added. Mathematically, if A\mathbf{A} and B\mathbf{B} are two vectors of equal magnitude but opposite directions, then:
A+B=0\mathbf{A} + \mathbf{B} = \mathbf{0}
This means the resultant of the two vectors will be zero. For example, if two forces of equal magnitude act in exactly opposite directions, the net force (resultant) will be zero.
Conclusion for C: Correct
Option D: Yes, when the two vectors are the same in magnitude making an angle of 2π3\frac{2\pi}{3} with each other
When two vectors of the same magnitude form an angle of 2π3\frac{2\pi}{3} (120 degrees) between them, the resultant will not be zero. In this case, the vectors will add up to produce a resultant vector with a non-zero magnitude. The condition for the resultant to be zero is when the vectors are directly opposite in direction (i.e., the angle between them is π\pi or 180 degrees).
Conclusion for D: Incorrect
Final Conclusion:
The resultant of two vectors can be zero when the vectors are same in magnitude but opposite in direction.
Thus, the correct answer is:
C. Yes, when the two vectors are same in magnitude but opposite in sense.
