Math and Arithmetic

Physics

Algebra

# Can a vector have a component greater than its magnitude?

###### Wiki User

###### January 15, 2008 12:53PM

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

## Related Questions

###### Asked in Math and Arithmetic, Physics, Algebra

### Can the magnitude of a vector be lesser than its component?

No, because the components along any other direction is v*cos(A)
where v is the magnitude of the original vector and A is the angle
between the direction of the original vector and the direction of
the component.
Since the absolute value of cos(A) cannot be greater than 1,
then v*cos(A) cannot be greater than v.

###### Asked in Math and Arithmetic, Physics, Algebra

### Can the magnitude of a vector be less than magnitudes both of components?

The magnitude of the sum of any two vectors can be anywhere
between zero and
the sum of their two magnitudes, depending on their magnitudes
and the angle
between them.
When you say "components", you're simply describing a sum of two
vectors that
happen to be perpendicular to each other. In that case, the
magnitude of their
sum is
Square root of [ (magnitude of one component)2 + (magnitude of
the other component)2 ]
It looks to me like that can't be less than the the magnitude of
the greater component.

###### Asked in Math and Arithmetic, Physics, Algebra

### Why component of vector is not greater than magnitude?

In two dimensions (to keep it simple), the magnitude is the
square root of (x2 + y2). This follows directly from Pythagoras'
Law. Now, experiment a bit with this formula, inserting some
numbers, to get a feel for how the magnitude depends on the
components.
Pythagoras' Law can be extended to 3 or more dimensions in an
analogous fashion.