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An ichthyologist is modeling the movement of a fish in a 3D aquatic environment using vector dynamics. Suppose the fish's velocity vector is \(\mathbf{v} = egin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}\) and the direction of the current is given by \(\mathbf{c} = egin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}\). Find the component of the fishҀ™s velocity perpendicular to the current direction.
The component of \(\mathbf{v}\) perpendicular to \(\mathbf{c}\) is given by:
\mathbf{v}_{\perp} = \mathbf{v} - ext{proj}_{\mathbf{c}} \mathbf{v}

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