Answer
$(a)\quad$ Makes sense.
$(b)\quad$ Does not make sense.
$(c)\quad$ Makes sense.
$(d)\quad$ Does not make sense.
Work Step by Step
$(a)\quad$
${\bf u}\times{\bf v} $ is a vector, ${\bf w}$ is a vector.
The dot product of two vectors is defined.
Makes sense.
$(b)\quad$
${\bf u}$ is a vector, but ${\bf v}\cdot{\bf w}$ is not.
The cross product is not defined for a vector and scalar.
Does not make sense.
$(c)\quad$
${\bf u} $ is a vector, $ {\bf v}\times{\bf w}$ is a vector.
The dot product of two vectors is defined.
Makes sense.
$(d)\quad$
${\bf v}\cdot{\bf w}$ is a scalar.
The scalar product is defined between two vectors.
${\bf u}$ is a vector, but ${\bf v}\cdot{\bf w}$ is not.
Does not make sense.
