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Can two vectors of different magnitude be combined to get zero resultant

Can two vectors of different magnitude be combined to get zero resultant

Grade:12

3 Answers

Arun
25750 Points
6 years ago
.Therefore the three vectors with different magnitude can give zero resultant.\tiny 2\widehat{i} + 3\widehat{i} - 5\widehat{i} = 0\widehat{i} is . \large \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} , such that the resultant vector\tiny \overrightarrow{c} = -5\widehat{i}, and\tiny \overrightarrow{a} = 2\widehat{i} ,\widehat{b} , = 3\widehat{i}No, two vectors with different magnitude can never give a zero resultant. This is because the effect of vectors cancels out only when they act in the opposite direction and have the same magnitude.Yes, three vectors with different magnitude can give a zero resultant. As an example consider vectors  RegardsArun (askIITians forum expert)
bharat
29 Points
6 years ago
no,we can not have two vectors having different magnitude but resultant zero since if we see the resultant of two vectors at an angle \Theta then it is equal to v resultant= sqrt(v1^2+v2^2+2v1v2cos\Theta) ,as we see that only the factor containing \Theta can only be zero for \Theta =90 and thus it is not possible to have two vectors having diff magnitude ,resultant =zero. but it may be possible in case 3 dimensional vectors.
Lakshita
12 Points
6 years ago
Yes it is possible that the 2 vectors of different magbitude be combined to get 0 resultant because 2 vectors ar perpendicular to each other and their resultant follows the parellelogram of vector addition

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