Question

If $\overline{a},\overline{b},\overline{c}$ are three non-coplanar, non-zero vectors and $\overline{r}$ is any vector then $\overline{r}$ can be represented as $x\overline{a}+y\overline{b}+z\overline{c}$

• A. always
• B. never
• C. is one and only one way
• D. None of these

Answer 1

Answer: (C)

is one and only one way

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three non-coplanar, non-zero vectors and $\overrightarrow{r}$ is any vector then $\overrightarrow{r}$ can be represented as a linear combination of these vectors in a unique way.
i.e $\overrightarrow{r}=x\overrightarrow{a}+y\overrightarrow{b}+x\overrightarrow{c}$ where $x,y,z$ are scalar quantities.
Hence, option B is correct.