## Thomas' Calculus 13th Edition

$(a)\quad$ Makes sense. $(b)\quad$ Does not make sense. $(c)\quad$ Makes sense. $(d)\quad$ Does not make sense.
$(a)\quad$ ${\bf u}\times{\bf v}$ 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.