JEE Advance - Mathematics (1985 - No. 5)
If $$\overrightarrow A = \left( {1,1,1} \right),\,\,\overrightarrow C = \left( {0,1, - 1} \right)$$ are given vectors, then a vector $$B$$ satifying the equations $$\overrightarrow A \times \overrightarrow B = \overrightarrow {\,C} $$ and $$\overrightarrow A .\overrightarrow B = \overrightarrow {3\,} $$ ..........
$$\frac{5}{3}\widehat i + \frac{2}{3}\widehat j + \frac{2}{3}\widehat k$$
$$\frac{2}{3}\widehat i + \frac{5}{3}\widehat j + \frac{2}{3}\widehat k$$
$$\frac{2}{3}\widehat i + \frac{2}{3}\widehat j + \frac{5}{3}\widehat k$$
$$\widehat i + \widehat j + \widehat k$$
$$\widehat i - \widehat j + \widehat k$$