Vectors question?

Question

can you answer this question Can a vector have a component greater than its magnitude?

Answer 1

Look at it this way:

In 3-d, the magnitude squared of a vector, v, is:

|v|^2 = vx^2 +vy^2 +vz^2

Since none of the elements on the right can be negative, this implies that for ANY vector:

|v| >= vx or vx <= |v| and
|v| >= vy
|v| >= vy

The equalities hold when there is exactly one component of the vector.

Answer 2

Nope

Answer 3

No, this is impossible.

It's like having a right triangle with one of the legs longer than the hypothenuse.