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mosquitoes and bug bugNo, the resultant of two equal vectors will have a magnitude that is not equal to the magnitude of the original vectors. When two vectors are added together, the resulting vector will have a magnitude that depends on the angle between the two vectors.
No, the sum of two vectors cannot be a scalar.
The magnitudes of two vectors are added when the vectors are parallel to each other. In this case, the magnitude of the sum is equal to the sum of the magnitudes of the two vectors.
The range of possible values of the resultant of two vectors is from the magnitude of the difference of the magnitudes of the two vectors to the sum of the magnitudes of the two vectors. This range occurs when the two vectors are in the same direction or in opposite directions, respectively.
Two vectors: no. Three vectors: yes.
Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.
false
The gradient of the dot product of two vectors is equal to the sum of the gradients of the individual vectors.
Yes.
No, the sum of two vectors cannot be equal to either of the vectors. Adding two vectors results in a new vector, with a magnitude and direction that is determined by the individual vectors being added.
No, the sum of two vectors cannot be equal to either of the vectors individually. In vector addition, the resultant vector is determined by the magnitude and direction of the individual vectors. The sum of two vectors represents the combination of their effects, resulting in a new vector with different properties than the original vectors.
Sure, if the two vectors point in the same direction.When we need the sum of magnitudes of two vectors we simply add the magnitudes, but to get the magnitude of the sum of these two vectors we need to add the vectors geometrically.Formula to find magnitude of the sum of these two vectors is sqrt[ |A|2 +|B|2 +2*|A|*|B|*cos(z) ] where |A| and |B| are magnitudes of two A and B vectors, and z is the angle between the two vectors.Clearly, magnitude of sum of two vectors is less than sum of magnitudes(|A| + |B|) for all cases except when cos(z)=1(for which it becomes = |A| + |B| ). Cos(z)=1 when z=0, i.e. the vectors are in the same direction(angle between them is 0).Also if we consider addition of two null vectors then their sum is zero in both ways of addition.So, we get two caseswhen the two vectors are in same direction, andwhen the two vectors are null vectors.In all other cases sum of magnitudes is greater than magnitude of the sum of two vectors.