Question

Force $\overrightarrow{F}$ applied on a body is written as $\overrightarrow{F}=(\hat{n}\cdot \hat{f})\hat{n}+\overrightarrow{G}$, where $\hat{n}$ is a unit vector. The vector $\overrightarrow{G}$ is equal to.

• A. $\hat{n}\times \overrightarrow{F}$
• B. $\hat{n}\times (\hat{n}\times \overrightarrow{F})$
• C. $(\hat{n}\times \overrightarrow{F})\times \overrightarrow{F}/|\overrightarrow{F}|$
• D. $(\hat{n}\times \overrightarrow{F})\times \hat{n}$

Answer 1

Answer: (D)

$(\hat{n}\times \overrightarrow{F})\times \hat{n}$

$(\overline{n}.\overline{f})\overline{n}=0$

Because in scalar triple product if two vectors are equal value of scalar triple product is 0.

$\therefore \overrightarrow{F}=\overrightarrow{G}$,

But $F=(\overline{n}\times \overrightarrow{F})\times \overline{n}$

Because $\overline{n}$ is unit vector.

$\therefore \overrightarrow{G}=(\overline{n}\times \overrightarrow{F})\times \overline{n}$