Why vector quantities cannot be added and subtracted like scalar quantities?

Answer 1

Mainly because they aren't scalar quantities.

A vector in the plane has two components, an x-component and a y-component. If you have the x and y components for each vector, you can add them separately. This is very similar to the addition of scalar quantities; what you can't add directly, of course, is their lengths.

Similarly, a vector in space has three components; you can add each of the components separately.

Answer 2

Vector quantities have both magnitude and direction, so simple addition or subtraction is not enough to combine them. Instead, vector addition requires considering both magnitude and direction using mathematical rules such as the parallelogram law. Scalars, on the other hand, only have magnitude and can be added or subtracted in a straightforward manner.

Answer 3

Vector quantities cannot be added or subtracted like scalar quantities because a vector in the plane has two components : x and y. You can add vector quantities separately but you can not add their lengths directly.

Hope this helped!