Let \(\overline{OA} = \overline{i} + 2\overline{j} + 2\overline{k}\), \(\overline{OB} = 3\overline{i} + 4\overline{k}\). If \(x\overline{i} + y\overline{j} + z\overline{k}\) is the vector along the bisector of \(\angle AOB\) and of length 2 units, then a possible value of \(x + y + z\) is:
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For angle bisector vectors, always compute unit vectors first, then simplify before scaling—this avoids messy radicals.