jee-main 2015 Q87

jee-main · India · 04apr Vectors Introduction & 2D Angle or Cosine Between Vectors
Let $\vec { a } , \vec { b }$ and $\vec { c }$ be three non-zero vectors such that no two of them are collinear and $( \vec { a } \times \vec { b } ) \times \vec { c } = \frac { 1 } { 3 } | \vec { b } | | \vec { c } | \vec { a }$. If $\theta$ is the angle between vectors $\vec { b }$ and $\vec { c }$, then a value of $\sin \theta$ is
(1) $\frac { - 2 \sqrt { 3 } } { 3 }$
(2) $\frac { 2 \sqrt { 2 } } { 3 }$
(3) $\frac { - \sqrt { 2 } } { 3 }$
(4) $\frac { 2 } { 3 }$
Let $\vec { a } , \vec { b }$ and $\vec { c }$ be three non-zero vectors such that no two of them are collinear and $( \vec { a } \times \vec { b } ) \times \vec { c } = \frac { 1 } { 3 } | \vec { b } | | \vec { c } | \vec { a }$. If $\theta$ is the angle between vectors $\vec { b }$ and $\vec { c }$, then a value of $\sin \theta$ is\\
(1) $\frac { - 2 \sqrt { 3 } } { 3 }$\\
(2) $\frac { 2 \sqrt { 2 } } { 3 }$\\
(3) $\frac { - \sqrt { 2 } } { 3 }$\\
(4) $\frac { 2 } { 3 }$