Vectors and matrices › Lines, planes and vectors in space › Angles between vectors and planes

Sine of angle from triple product

High school · ●●●○○ 50 pts

Let

\mathbf{a},

\mathbf{b},

and

\mathbf{c}

be nonzero vectors, no two of which are parallel, such that

(\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = \frac{1}{3} \|\mathbf{b}\| \|\mathbf{c}\| \mathbf{a}.

Let

\theta

be the angle between

\mathbf{b}

and

\mathbf{c}.

Find

\sin \theta.

Round to two decimal places.

vector triple product cross product dot product angle between vectors