Question

If $\hat{a}$ and $\hat{b}$ are orthogonal unit vectors then for any non zero vector $\overrightarrow{r}$, the vector $(\overrightarrow{r}\times \hat{a})$ equals

• A. $\left[\overrightarrow{r}\hat{a}\hat{b}\right](\hat{a}\times \hat{b})$
• B. $\left[\overrightarrow{r}\hat{a}\hat{b}\right]\hat{a}+(\overrightarrow{r}\cdot \hat{a})(\hat{a}\times \hat{b})$
• C. $\left[\overrightarrow{r}\hat{a}\hat{b}\right]\hat{b}+(\overrightarrow{r}\cdot \hat{b})(\hat{b}\times \hat{a})$
• D. $\left[\overrightarrow{r}\hat{a}\hat{b}\right]\hat{b}+(\overrightarrow{r}\cdot \hat{a})(\hat{a}\times \hat{b})$

Answer 1

The correct option is A $\left[\overrightarrow{r}\hat{a}\hat{b}\right](\hat{a}\times \hat{b})$

the given question has option typing problem

It is $\left[\overrightarrow{r}\hat{a}\hat{b}\right](\hat{a}\times \hat{b})$

given

$\hat{a}\times \hat{b}=1$-----(1)

$\overrightarrow{r}\times \overrightarrow{a}$

dot product with b

$(\overrightarrow{r}\times \overrightarrow{a})\times \hat{b}$

$\left[\overrightarrow{r}\overrightarrow{a}\hat{b}\right]$

$\left[\overrightarrow{r}\overrightarrow{a}\hat{b}\right]\left(1\right)$

form eq (1)

$\left[\overrightarrow{r}\overrightarrow{a}\hat{b}\right](\overrightarrow{a}\times \overrightarrow{b})$