A vector A has size 6 and points east. Give the size and the direction of 2A and of -1/2A…

Step 1. Multiples. $2\vec{A}$ has size $12$ and points east. $-\tfrac{1}{2}\vec{A}$ has size $3$ and points west: the minus sign turns it round.

Step 2. The size of B. $B = \sqrt{5^2 + (-12)^2} = \sqrt{169} = 13$.

Step 3. The unit vector. $\hat{B} = \dfrac{5\hat{i} - 12\hat{j}}{13} = 0.385\hat{i} - 0.923\hat{j}$.

Step 4. The velocity. $\vec{v} = 26\,\hat{B} = 26 \times \dfrac{5\hat{i} - 12\hat{j}}{13} = (10\hat{i} - 24\hat{j})\ \text{m/s}$.