Question

What are common mistakes students make with 2-D vectors?

Answer 1

See explanation below

Explanation:

Common mistakes are not actually very common. This depends on a particular student. However here are a few probable mistakes which a student can make with 2-D vectors

1.) Misunderstand the direction of a vector.

Example: `vec{AB}` represents the vector of length `AB` which is directed from point `A` to point `B` i.e. point `A` is tail & point `B` is head of `\vec{AB}`

2.) Misunderstand the direction of a position vector

Position vector of any point say `A` always has the tail point at the origin `O` & head at the given point `A`

3.) Misunderstand the direction of vector product `\vec A\times \vec B`

Example: The direction of `\vec A\times \vec B` is given by right hand screw rule. Before applying right hand screw rule, the point to be noted is that both the vectors `\vec A` & `\vec B` must converging or diverging at the point of intersection.

Note: Two non parallel vectors can be made intersecting by shifting them in their respective parallel directions

There may be other common mistakes as well but above are few of them .