Motion in a Plane

A scalar quantity has magnitude only

A scalar quantity has magnitude only and is described by a single number with unit. A vector quantity has both magnitude and direction and follows the

The position vector r joins

The position vector r joins the chosen origin O to the position P of a particle. In two dimensions, it is written as r = x î + y ĵ, and in three dimen

The displacement vector is the straight

The displacement vector is the straight-line vector from the initial position to the final position. It is given by Δr = r' - r and does not depend on

The unit vectors î

The unit vectors î, ĵ, and k̂ have magnitude 1 and point along the x-, y-, and z-axes. They specify direction only and have no unit or dimension.

A vector A in a plane

A vector A in a plane can be written as A = Ax î + Ay ĵ. If A makes an angle θ with the x-axis, then Ax = A cosθ and Ay = A sinθ. Conversely, A = √(Ax