Let $$\overrightarrow A ,\overrightarrow B $$ and $${\overrightarrow C }$$ be unit vectors suppose that $$\overrightarrow A .\overrightarrow B = \overrightarrow A .\overrightarrow C = 0,$$ and thatthe angle between $${\overrightarrow B }$$ and $${\overrightarrow C }$$ is $$\pi /6.$$ Then $$\overrightarrow A = \pm 2\left( {\overrightarrow B \times \overrightarrow C } \right).$$

The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow A + \overrightarrow B + \overrightarrow C } \right)$$ equals :

Find the area bounded by the curve $${x^2} = 4y$$ and the straight

The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1$$ represents