Question
If . and $$ \times $$ represent dot product and cross product respectively then which of the following is meaningless?
A.
$$\left( {\overrightarrow a \times \overrightarrow b } \right).\left( {\overrightarrow c \times \overrightarrow d } \right)$$
B.
$$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow c \times \overrightarrow d } \right)$$
C.
$$\left( {\overrightarrow a .\overrightarrow b } \right)\left( {\overrightarrow c \times \overrightarrow d } \right)$$
D.
$$\left( {\overrightarrow a .\overrightarrow b } \right) \times \left( {\overrightarrow c \times \overrightarrow d } \right)$$
Answer :
$$\left( {\overrightarrow a .\overrightarrow b } \right) \times \left( {\overrightarrow c \times \overrightarrow d } \right)$$
Solution :
$$\overrightarrow a .\overrightarrow b $$ is a scalar and $$\overrightarrow a \times \overrightarrow b $$ is a vector. Dot or cross product is applicable for vectors only. Also, a vector may have a scalar multiple.