Answer
TRUE
Work Step by Step
Cross product is also known as vector product which is perpendicular to two vectors , therefore, it must also be perpendicular to either vector , that is , $u$ is orthogonal to $u\times v$.
Consider $u=( u_{1},u_{2},u_{3})$ and $v=( v_{1},v_{2},v_{3})$ then
$(u\times v).u=( u_{2}v_{3}-u_{3}v_{2},- (u_{1}v_{3}-u_{3}v_{1}), u_{1}v_{2}-u_{2}v_{1})( u_{1},u_{2},u_{3})$
$=u_{1}( u_{2}v_{3}-u_{3}v_{2})- u_{2}(u_{1}v_{3}-u_{3}v_{1})+u_{3}(u_{1}v_{2}-u_{2}v_{1})$
$=u_{1}u_{2}v_{3}-u_{1}u_{3}v_{2}- u_{2}u_{1}v_{3}+u_{2}u_{3}v_{1}+u_{3}u_{1}v_{2}-u_{3}u_{2}v_{1}$
Therefore, $(u\times v).u=0$
Hence, the statement is true.
