Can any of the component of a given vector have a greater magnitude than that of the vector itself?

Can any of the component of a given vector have a greater magnitude than that of the vector itself?

No, any rectangular component of a vector can not have magnitude more than the vector itself. As the name suggests, it’s a component of the vector. A component can not be larger than the whole thing.

How are the components of a vector related to its magnitude?

In the geometric interpretation of a vector the vector is represented by an arrow. The arrow has two parts that define it. The two parts are its length which represents the magnitude and its direction with respect to some set of coordinate axes. The greater the magnitude, the longer the arrow.

Can the magnitude of the resultant of two vectors be less than the magnitude of any of the vector?

Reason: The magnitude of the resultant vector of two given vectors can never be less than the magnitude of any of the given vector.

What is the maximum no of components into which a vector can be split?

(EXPLANATION :- in a plane you’re moving either in horizontal direction or vertical direction or both ). (EXPLANATION :-A vector can be split into infinite number of components.

Can the component of a vector be greater than the component?

Yes it can be. If we consider only orthogonal projections… then the component can never be greater. But if it is not mentioned that only orthogonal projections are required.. then we can break the vector into any two vectors.

Is the magnitude of component of a vector equal to Cos(Theta)?

No, magnitude of component of vector is given by multiplying the vector to cos(theta). Since value of cos always gives -1<1.

Is it possible to break a vector into two vectors?

But if it is not mentioned that only orthogonal projections are required.. then we can break the vector into any two vectors. In such case one can obtain the magnitude of component greater than the vector itself. For example we can break a vector 5i as 6i+ (-i),where ‘i’ is the unit vector.

How to find the magnitude of a vector in R^3?

To find out the magnitude for a vector in R^3, for example, you will have to sum the square roots of the components,and then take the square of the sum, like in this formula M^2=(x)^2+(y)^2+(z)^2. (M is the magnitude of the vector).