Question

Which of the following expressions are meaningfull operations?

• A. $\overrightarrow{u}.(\overrightarrow{v}\times\overrightarrow{w})$
• B. $(\overrightarrow{u}.\overrightarrow{v}).\overrightarrow{w}$
• C. $(\overrightarrow{u}.\overrightarrow{v})\overrightarrow{w}$
• D. $\overrightarrow{u}\times(\overrightarrow{v}.\overrightarrow{w})$

Answer 1

Answer: (C)

$(\overrightarrow{u}.\overrightarrow{v})\overrightarrow{w}$

Answer 2

$\overrightarrow{u}.(\overrightarrow{v}\times\overrightarrow{w})$ is a meaningful operation. Therefore, (a) is the answer. $\overrightarrow{u}.(\overrightarrow{v}.\overrightarrow{w})$ is not meaningful, since $\overrightarrow{v}.\overrightarrow{w}$ is a scalar quantity and for dot product both quantities should be vector. Therefore, (b) is not the answer. $\overrightarrow{u}.(\overrightarrow{v}).\overrightarrow{w}$ is meaningful, since it is a simple multiplication of vector and scalar quantity. Therefore, (c) is the answer. $\overrightarrow{u}\times(\overrightarrow{v}).\overrightarrow{w})$ is not meaningful, since $\overrightarrow{v}).\overrightarrow{w}$ is a scalar quantity and for cross product, both quantities should be vector. Therefore, (d) is not the answer.