Question

Can the magnitude of a vector be equal to the magnitude of one of its x or y components? Explain.

Can it be less than the magnitude of either the x component or the y component? Explain.

Answer 1

yes magnitude of a vector be equal to the magnitude of one of its x or y components

This is when vector is directed along any axis. Lets say x axis

Then magnitude of vector is equal to x component as y component is 0

No, it can’t be less than the magnitude of either the x component or the y component

This is because of law of triangle

x component, y component and magnitude of vector forms of a triangle

magnitude = sqrt(x^2+y^2)

It can never be less than x or y from above expression