can a vector have a component greater than its magnitude ? Explain?
Can a vector have a component that is greater than its magnitude? Please explain your reasoning.
6 Answers
No but it can have a component equal to its magnitude. If it is a 2D vector the magnitude is found by:
sqrt(x^2 + y^2) = magnitude
x, y are the horizontal and vertical components.
The reason that it can't be greater is that when you join the orthorgonal vectors from head to tail, it forms a right angled triangle, and the hypotenuse is always greater than its sides.
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can a vector have a component greater than its magnitude ? Explain?
No,the components of a vector cannot have magnitudes greater than the magnitudes of the vector itself because components is always a part of the resultant vector of the magnitude of the components will be less than that of resultant vector of course,if the two vectors of the same magnitude act at an angle of degree 120 with each other than vector
C = A + B [C] = [A] = [B]Where modulus vector [C] , [A] , [B] indicate the magnitudes of vector C ,A ,B respectively. Hence, the maximum value of magnitudes of the resultant vector.
Jan 27, 2025
See dear friend, when u resoolve any vector in two or more perpendicular components, there is always a factor cos theta or sin theta multiplied by the magnitude of the original vector. And u must know the maximum value of sin or cos theta is 1, so in any case the component of a vector can't be greater then the magnitude of the original vector. I think it is clear for u.
Regards
Anoop
it depends on your components. If they are ijk then the answer is no. but why cant you take your components to be different vectors. Then you could add you components up and actually get a zero magnitude from nonzero comps.
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