Mathematics

Problem

Let the cosine of angle between the vectors

\mathbf{p}

and

\mathbf{q}

\lambda

such that

2\mathbf{p} + \mathbf{q} = \hat{i} + \hat{j}

and

\mathbf{p} + 2\mathbf{q} = \hat{i} - \hat{j}

, then

\lambda

is equal to a.

\frac{5}{9}

-\frac{4}{5}

\frac{3}{9}

\frac{7}{9}