What are the direction cosines of the vector from $A(2, -1, 3)$ to $B(4, 1, 2)$?

Explanation

1. 01

   $\overrightarrow{AB} = (4 - 2)\hat{i} + (1 + 1)\hat{j} + (2 - 3)\hat{k} = 2\hat{i} + 2\hat{j} - \hat{k}$, of magnitude $\sqrt{4 + 4 + 1} = 3$.

2. 02

   Divide each component by 3: $\frac{2}{3}, \frac{2}{3}, -\frac{1}{3}$.