can a vector have a component greater than the vectors magnitude?

Never. A vector's magnitude is solved using the pythagorean theorem with the triangle's hypotenuse representing the vector's magnitude. The y component represents the vertical leg of the triangle and the x-component represents the horizontal leg of the triangle. It should always be a right triangle. In a right triangle, the hypotenuse is always the longest side and it can be solved using:

hypotenuse or vector's magnitude = sqrt (square of vertical leg + square of the horizontal leg)

                              :-)

The Magnitude Of The Component Of a vector Can't be Greater Then The magnitude of Vector If they Are The Rectangular Components

If the Components Are Not rectangular Components Then The Magnitude Of components May or may not Be greater then the Magnitude Of vector

Yes.

Vectors into which the given vector is resolved are called components of the given vector.

The rectangular components of a vector R are taken as

Rcosθ and Rsinθ where θ is the angle made by the vector with X axis. These cannot be greater than R in magnitude.

If you take two vectors of magnitude 5 and - 3 acting along +X and - X directions . Their resultant is of magnitude 2 along +X direction . In that case both the components are greater than the resultant .

No, the magnitude vector will always be larger than its component magnitudes, since the magnitude of the vector is the square root of the sum of the squares of the component vectors. Hope this helps.

As you want to resolve the vectors into two perpendicular components, then those two would be the opposite and adjacent sides of a right angled triangle with the very vector being the hypotenuse. In a right angled triangle, no one side can be greater than the hypotenuse. Hence the answer.

We take X and Y aspects of a V vector as V sin Ø and V cos Ø. Ø can selection from 0 to ninety stages. As Ø is going 0 ---> ninety sin Ø is going 0 ---> a million cos Ø is going a million ---> 0 optimal cost of sin Ø is a million while the attitude is ninety stages. So the optimal X factor could be V sin ninety = V while the factor it ninety stages to the vector. optimal cost of cos Ø is a million while the attitude is 0 stages. So the optimal Y factor could be V cos 0 = V while the factor it 0 stages to the vector. So neither factor could have a miles better cost than the vector itself has.

No, the component of a vector can not have magnitude greater than the magnitude of the vector itself. Because the component is always a part of the vector. If two vectors of the same magnitude act as an angle of 120 degree with each other, then

           R  =   P  +  Q

Hence, the maximum value of the magnitude of component can be equal to the magnitude of the resultant vector.

no , it is not possible to say.bcoz always magnitude of the vector comes +ve.