why do we say that force is a vector quantity

What is the definition of the term "vector quantity"? A vector quantity is a quantity of something which possesses both magnitude and direction. Magnitude is simply the size or amount of the quantity. For exam. What Is Magnitude in Physics? In physics, magnitude generally refers to distance or quantity. In relation to movement, magnitude refers to the size of an object or its speed while trave. What is the relationship between acceleration and velocity? Acceleration shows the changes in the magnitude and direction of velocity. It is a vector with a standard unit of meters per second squared.

What is the difference betwen scalar versus vector quantities? The difference between scalar and vector quantities is that the former only provides numerical data or magnitude, while the latter also provides direction.
Vectors are things that add like little arrows. Arrows add tip to tail. Number of rocks is not a vector. 2 rocks + 2 rocks = 4 rocks. Displacement is a vector. If you move 2 feet left and 2 feet left again, you have moved 4 feet. Two arrows 2 feet long pointing left added tip to tail are equivalent to one arrow 4 feet long pointing left.

If you move 2 feet left and 2 feet right, you have moved back to the start. This is the same a not moving at all. You can't add rocks this way. Force adds like this. Two small forces to the left are equivalent to a big force to the left. Equal forces left and right are equivalent to no force. This is why force is a vector. Edit - The comments raise a point that I glossed over. This point is usually not raised when introducing vectors. Mathematicians define a vector as things that behave like little arrows when added together and multiplied by scalars.

Physicists add another requirement. Vectors must be invariant under coordinate system transformations. A little arrow exists independently of how you look at it. A little arrow does not change when you turn so it is now facing forward. Equivalently, little arrows do not change if you rotate the arrow so that it faces forward. This is because space is homogeneous and isotropic. There are no special places or directions in space that would change you or an arrow if moved to a new location or orientation. (If you move away from Earth gravity is different.

If this matters, you must move Earth too. ) By contrast, a scalar is a single number that does not change under coordinate system transformations. Number of rocks is a scalar. The coordinates that describe a vector change when the coordinate system is changed. The left component of a vector is not a scalar. There is a 1-D mathematical vector space parallel to the left coordinate of a vector. If you rotate the coordinate system, it may be parallel to what has become the forward component. A physicist would not say it is a vector space.

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