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For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer
let $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ be two unit vectors such that $$\overrightarrow{a} .\overrightarrow{b}$$ =0 For some $$X,y \in R$$ let $$\overrightarrow{C}$$=X$$\overrightarrow{a}$$+Y$$\overrightarrow{b}$$+$$(\overrightarrow{a} \times \overrightarrow{a})$$.If $$ \mid \overrightarrow{c} \mid$$=2 and the $$\overrightarrow{c}$$ is inclined at the same angle $$\alpha$$ to both $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$,then the value of $$8 \cos^{2} \alpha$$ is .......
Correct Answer: e
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