Unit vector r which satisfies r b = r c where b = i + 2 j + k & c… - Vidyadip

MCQ

Unit vector $\vec r$ which satisfies $\vec r \times \vec b = \vec r \times \vec c$ where $\vec b = \hat i + 2\hat j + \hat k$ & $\vec c = 3\hat i + 2\hat k$ , is

✓
$ \pm \left( {\frac{{2\hat i - 2\hat j + \hat k}}{3}} \right)$
B
$ \pm \left( {\frac{{2\hat i + 2\hat j + \hat k}}{3}} \right)$
C
$ \pm \left( {\frac{{\hat i + \hat j + \hat k}}{{\sqrt 3 }}} \right)$
D
$ \pm \,\hat i$

✓

Answer

Correct option: A.

$ \pm \left( {\frac{{2\hat i - 2\hat j + \hat k}}{3}} \right)$

a
$(\vec{r} \times \vec{b})-(\vec{r} \times \vec{c})=\overrightarrow{0} \Rightarrow \vec{r} \times(\vec{b}-\vec{c})=\overrightarrow{0}$

$ \Rightarrow \vec r = \lambda (\vec b - \vec c) = \lambda ( - 2\hat i + 2\hat j - \hat k)$

$ \Rightarrow \hat r = \pm \left( {\frac{{2\hat i - 2\hat j + \hat k}}{3}} \right)$

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