Question

If the non-zero vector $\overline{a}$ and $\overline{b}$ are perpendicular to each other, then the solution of the equation $\overline{r}\times \overline{a}=\overline{b}$ is

• A. $\overline{r}=x\overline{a}+\frac{1}{\overline{a}.\overline{a}}(\overline{a}\times \overline{b})$
• B. $\overline{r}=x\overline{b}+\frac{1}{\overline{b}.\overline{b}}(\overline{a}\times \overline{b})$
• C. $\overline{r}=x(\overline{a}\times \overline{b})$
• D. $Noneofthese$

Answer 1

The correct option is A $\overline{r}=x\overline{a}+\frac{1}{\overline{a}.\overline{a}}(\overline{a}\times \overline{b})$

Given non-zero vector $\overline{a}and\overline{b}$ are perpendicular to each other.

equation is , $\begin{array}{c}\overline{r}\times \overline{a}=\overline{b},\\ \Rightarrow \frac{\overline{a}\times (\overline{r}\times \overline{a})}{\overline{a}.\overline{a}}=\frac{\overline{a}\times \overline{b}}{\overline{a}.\overline{a}}\end{array}$

$\begin{array}{c}\Rightarrow \frac{\overline{(a}\times \overline{a})\overline{r}}{\overline{a}.\overline{a}}-\frac{\overline{(a}\times \overline{r})\overline{a}}{\overline{a}.\overline{a}}=\frac{\overline{a}\times \overline{b}}{\overline{a}.\overline{a}}\\ \overline{r}=\frac{\overline{(a}\times \overline{r})\overline{a}}{\overline{a}.\overline{a}}+\frac{\overline{a}\times \overline{b}}{\overline{a}.\overline{a}}\\ \therefore \overline{r}=\overline{x}.\overline{a}+\frac{1}{\overline{a}.\overline{a}}(\overline{a}\times \overline{b})\end{array}$

therefor the correct option is A.