Let $\vec { a }$ and $\vec { b }$ be the vectors along the diagonal of a parallelogram having area $2 \sqrt { 2 }$. Let the angle between $\vec { a }$ and $\vec { b }$ be acute. $| \vec { a } | = 1$ and $| \vec { a } \cdot \vec { b } | = | \vec { a } \times \vec { b } |$. If $\vec { c } = 2 \sqrt { 2 } ( \vec { a } \times \vec { b } ) - 2 \vec { b }$, then an angle between $\vec { b }$ and $\vec { c }$ is (1) $\frac { - \pi } { 4 }$ (2) $\frac { 5 \pi } { 6 }$ (3) $\frac { \pi } { 3 }$ (4) $\frac { 3 \pi } { 4 }$
Let $\vec { a }$ and $\vec { b }$ be the vectors along the diagonal of a parallelogram having area $2 \sqrt { 2 }$. Let the angle between $\vec { a }$ and $\vec { b }$ be acute. $| \vec { a } | = 1$ and $| \vec { a } \cdot \vec { b } | = | \vec { a } \times \vec { b } |$. If $\vec { c } = 2 \sqrt { 2 } ( \vec { a } \times \vec { b } ) - 2 \vec { b }$, then an angle between $\vec { b }$ and $\vec { c }$ is\\
(1) $\frac { - \pi } { 4 }$\\
(2) $\frac { 5 \pi } { 6 }$\\
(3) $\frac { \pi } { 3 }$\\
(4) $\frac { 3 \pi } { 4 }$