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Can a component of a vector be greater than the vector's magnitude?
Wiki User
∙ 11y ago
No. If the vector is 2D then it's magnitude is (x^2+y^2)^0.5 where x and y are the components and ^0.5 means take the square root. In 3D this becomes (x^2+y^2+z^2)^0.5 etc. Thus the magnitude is always at least as big as one of the components.
Here's an example of a 3D vector: (3,4,5)
|(3,4,5)|=(3^2+4^2+5^2)^0.5=(9+16+25)^0.5=50^0.5=7.07...
If y and z were 0: (3,0,0)
|(3,0,0)|=(3^2+0^2+0^2)^0.5=(9+0+0)^0.5=9^0.5=3 ie the magnitude is the same size as x.
You can also consider this geometrically. A vector is an arrow and the magnitude represents the length of the arrow. Vector addition is the 'adding' of these arrows so (3,4,5)=(3,0,0)+(0,4,0)+(0,0,5). Clearly the length of an arrow built of three smaller ones can't be less than any one of them.
Wiki User
∙ 11y ago
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Can a vector have a component greater than the magnitude of vector?
no a vector cannot have a component greater than the magnitude of vector
Can a vector have a component greater than the magnitude?
No.
Can the magnitude of a resultant vector be greater than the sum of individual vectors?
The resultant vector IS the sum of the individual vectors. Its magnitudecan be the sum of their individual magnitudes or less, but not greater.
Can a vector have a component greater than its magnitude?
No a vector may not have a component greater than its magnitude. When dealing with highschool phyics problems, the magnitude is usually the sum of two or more components and one component will offset the other, causing the magnitude to be less then its component
Can a vector have a component greater than its magnitude in higher level physics?
yeah, it can. for example consider two antiparallel vectors of magnitude 5,3 whose resultant is 2, which is smaller than both components.....
Vector component greater than the vectors magnitude?
A vector component can never be greater than the vector's magnitude. The magnitude of a vector is the length of the vector and is always greater than or equal to any of its individual components.
Can a vector have a component greater than vectors magnitude?
No.
Can a vector have a component greater than the magnitude of vector?
no a vector cannot have a component greater than the magnitude of vector
Can a vector have a component greater than the vector's magnitude?
No, a vector's component cannot be greater than the vector's magnitude. The magnitude represents the maximum possible magnitude of a component in any direction.
Can a vector have a component greater than the magnitude of the vector?
No, a vector component is a projection of the vector onto a specific direction. It cannot have a magnitude greater than the magnitude of the vector itself.
Can a component of vector greater than vector magnitude?
No, a component of a vector cannot be greater than the magnitude of the vector itself. The magnitude of a vector is the maximum possible value that can be obtained from its components.
Can the magnitude of the difference between two vectors ever be greater than the magnitude of either vector?
Yes, the magnitude of the difference between two vectors can be greater than the magnitude of either vector. This can occur when the vectors are in opposite directions or have different magnitudes such that the resulting difference vector is longer than either of the original vectors.
Can the component of a vector ever be greater than the magnitude of the vector?
No.
Can a vector have a component greater than it magnitude?
No.
Can a vector have a component greater than the magnitude?
No.
Can the magnitude of a resultant vector be greater than the sum of individual vectors?
The resultant vector IS the sum of the individual vectors. Its magnitudecan be the sum of their individual magnitudes or less, but not greater.
Can a vector have a component greater than its magnitude?
No a vector may not have a component greater than its magnitude. When dealing with highschool phyics problems, the magnitude is usually the sum of two or more components and one component will offset the other, causing the magnitude to be less then its component
