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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.
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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 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 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.
Can a unit vector have any components with magnitude greater than unity?
No, by definiton, a unit vector is a vector with a magnitude equal to unity.
