The component of a vector is : 1. Always less than its magnitude. 2. Always greater than its magnitude 3. Always equal to its magnitude 4. None of these.
I know the answer will be 4. I can understand very easily that the component of vector can be less than its magnitude for example in a right angles triangle the hypotenuse is longer than both sides or we can say componnet of A along a line will be A.cos(theta) which must be less than or equal to A. Hence it is also possible to have component equal to A when cos equals 1. But is it possible to have component of vector greater than itself? If we think of component as A.cos(theta) then it is not possible according to range of cosine function but if we consider it geometrically we can construct a parallelogram whose diagonal is shorter than its length of sides when angle between vectors is obtuse and large or we can also construct a triangle with third side shorter than either. Is it possible or is only less than or equal to the only possibilities. May someone help?