JEE-Advanced 2015 (19.A/40)

Geometry Level 3

In \(\mathbb R^2\) if the magnitude of the projection vector of the vector \(\alpha \hat +\beta \hat j\) on \(\sqrt3 \hat i +\hat j\) is \(\sqrt3\) and if \(\alpha=2+\sqrt3 \beta\), then find the possible value(s) of \(|\alpha|\). \[\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 3 & (4) \, 4 \end{array}\]

Note:

  • Submit your answer as the increasing order of the serial numbers of all the correct options.

  • For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.

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