Define and use unit vectors and the perpendicular unit vectors 𝒊̂ and 𝒋̂.

Which expression represents the unit vector in the direction of $\vec{v} = 5\hat{i} - 12\hat{j}$?

Given vectors **u** = 3**i** + 4**j** and **v** = –5**i** + 12**j**, determine: (a) the unit vector in the direction of **u** (b) the unit vector in the direction of **v** (c) Show that the vector **w** = (2**u** + 3**v**)/(|2**u** + 3**v**|) can be expressed in the form a**i** + b**j** where a, b ∈ ℝ, and determine the exact values of a and b.

Which expression represents the unit vector in the direction of the vector **u** shown in the diagram below?

Consider the vector $\mathbf{v} = 6\mathbf{\hat{i}} - 8\mathbf{\hat{j}}$. (a) Determine the magnitude of $\mathbf{v}$. (b) Hence determine the unit vector in the direction of $\mathbf{v}$, leaving your answer in terms of $\mathbf{\hat{i}}$ and $\mathbf{\hat{j}}$.