A vector changes if

1. its direction changes.
2. Any of these
3. its magnitude changes.
4. its direction and magnitude both
change.
5. None of these
i know it is not 3 or 4. Please explain it to me

Well, if you know it's not option 3 or 4, then that leaves us with options 1, 2, and 5. Let me give you a little hint: vectors aren't like moody teenagers, silently changing their minds for no reason. So, if it's not options 3 or 4, you can rule out any sudden flip-flopping in magnitude or direction. That leaves us with option 1 - a vector changes if its direction changes. So go ahead and pick that option, unless you want to consider the possibility that vectors have developed a secret love for surprising us, which would make option 2 equally valid.

A vector changes if either its direction changes or its magnitude changes, or both.

Direction refers to the line along which the vector points, while magnitude refers to the length or size of the vector.

For example, if you have a vector pointing north with a magnitude of 5 units, and then you change its direction to point east without changing its magnitude, it has undergone a change in direction. Similarly, if you keep the vector pointing north but change its magnitude to 10 units, it has undergone a change in magnitude.

So, a vector can change if either its direction or magnitude changes, or if both change simultaneously.

To determine which option is correct, let's consider the definition of a vector. A vector is a quantity that has both magnitude and direction. Therefore, any change in either the direction or magnitude of a vector will cause it to change.

Option 1 states that a vector changes if its direction changes. This is true because the direction is a fundamental characteristic of a vector, so any change in direction would result in a different vector.

Option 2 states that a vector changes if any of the mentioned conditions occur. Since option 1 is correct, it means that option 2 is also correct because a vector would change if either its direction or magnitude changes.

Option 3 states that a vector changes if its magnitude changes. This option is incorrect because a vector can remain the same even if its magnitude changes, as long as its direction remains unchanged.

Option 4 states that a vector changes if both its direction and magnitude change. This option is also incorrect because a vector can change even if only one of these quantities changes.

Therefore, the correct answer is option 2: a vector changes if any of the mentioned conditions occur, meaning its direction changes, its magnitude changes, or both.

You are wrong. A vector consists of a magnitude and direction. If either, or both change, the vector is changed.