A vector in the plane is expressed as

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

\mathbf{V}=V_x\,\mathbf{\hat{i}}+V_y\,\mathbf{\hat{j}}

. Answer the following questions related to this representation. (i) State what is meant by a unit vector with reference to

\mathbf{V}

. (ii) Show that the vector

\displaystyle \frac{\mathbf{V}}{|\mathbf{V}|}

has magnitude

1

, where

|\mathbf{V}|

denotes the magnitude of

\mathbf{V}

. (iii) Explain why the operation carried out in part (ii) keeps the direction of

\mathbf{V}

unchanged.