JEE Advance - Mathematics (1991 - No. 2)
Given that $$\overrightarrow a = \left( {1,1,1} \right),\,\,\overrightarrow c = \left( {0,1, - 1} \right),\,\overrightarrow a .\overrightarrow b = 3$$ and $$\overrightarrow a \times \overrightarrow b = \overrightarrow c ,$$ then $$\overrightarrow b \, = $$.........
$$\left( {\frac{5}{3},\frac{2}{3},\frac{2}{3}} \right)$$
$$\left( {\frac{2}{3},\frac{5}{3},\frac{2}{3}} \right)$$
$$\left( {\frac{2}{3},\frac{2}{3},\frac{5}{3}} \right)$$
$$\left( {\frac{1}{3},\frac{1}{3},\frac{1}{3}} \right)$$
$$\left( {\frac{5}{3},\frac{5}{3},\frac{5}{3}} \right)$$