Yes. A simple case would be a vector 2a acting at a point in one direction and two vectors, each of magnitude a, acting at the same point in the opposite direction.
Chat with our AI personalities
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
"If two vector quantities are represented by two adjacent sides or a parallelogram then the diagonal of parallelogram will be equal to the resultant of these two vectors."
The two vectors form the minor legs of a right angled triangle and the resultant is the hypotenuse of the triangle. Its magnitude, therefore, is the square root of the sum of the squared magnitudes of the two vectors.
When the component vectors have equal or opposite directions (sin(Θ) = 0) i.e. the vectors are parallel.