Calculate and use a unit vector, 𝒏̂, in the plane. 𝒏̂ = 𝒏 |𝒏|

Calculate the unit vector $\hat{\mathbf{n}}$ for the vector $\mathbf{n} = 5\mathbf{i} - 12\mathbf{j}$.

Two forces act on a particle moving in a plane: F₁ has magnitude 8.0 N at 30° (measured anticlockwise from the positive x-axis), and F₂ has magnitude 6.0 N at 150°. (a) Calculate the resultant force vector FR = F₁ + F₂. Express your answer in component form. (b) Determine the unit vector n̂ in the direction of the resultant force.

The displacement vector from point A to point B is given by **n** = 5**i** − 12**j**, where **i** and **j** are unit vectors in the *x*- and *y*-directions respectively. (a) Calculate |**n**|. (1 mark) (b) Calculate the unit vector **n̂** in the direction of **n**. (2 marks) (c) A particle moves from point C in the direction of **n̂** for a distance of 39 units. Calculate the displacement vector of the particle. (1 mark)

The diagram shows vector **p** in the plane with components **p** = 5**i** + 12**j**. Which of the following is the unit vector **p̂** in the direction of **p**?

A vector $\mathbf{p}$ has components $\mathbf{p} = 5\mathbf{i} - 12\mathbf{j}$. (a) Calculate the magnitude of $\mathbf{p}$. (b) Determine the unit vector $\hat{\mathbf{p}}$ in the direction of $\mathbf{p}$. (c) Calculate $3\hat{\mathbf{p}} \cdot \mathbf{p}$.