Define and use the magnitude and direction of a vector.

Consider the vector $\mathbf{v} = 3\mathbf{i} - 4\mathbf{j} + 12\mathbf{k}$. (a) Determine the magnitude of $\mathbf{v}$. (1 mark) (b) Hence, determine a unit vector in the direction of $\mathbf{v}$. (1 mark) (c) Determine the angle that $\mathbf{v}$ makes with the positive $z$-axis, correct to one decimal place. (1 mark)

Calculate the magnitude of the vector **u** = 5**i** − 12**j**.

A drone travels from point P to point Q. The displacement vector of the drone's flight path is given by vector PQ = 8i - 6j + 24k, where distances are measured in metres. Determine: (a) the magnitude of the displacement vector PQ (1 mark) (b) the unit vector in the direction of PQ, expressing your answer in the form ai + bj + ck, where a, b, and c are exact values (1 mark) (c) the angle, in degrees correct to one decimal place, that the displacement vector makes with the positive z-axis (1 mark)