JEE Advance - Mathematics (2007 - No. 13)
Let $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ be unit vectors such that $${\overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0 .}$$ Which one of the following is correct ?
$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a = \overrightarrow 0 $$
$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a \ne \overrightarrow 0 $$
$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow a \times \overrightarrow c \ne \overrightarrow 0 $$
$$\overrightarrow a \times \overrightarrow b ,b \times \overrightarrow c ,\overrightarrow c \times \overrightarrow a $$ are muturally perpendicular