A) \[\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\]
B) \[\frac{1}{\sqrt{5}}(2\hat{i}+\hat{j})\]
C) \[\pm \frac{1}{\sqrt{2}}(\hat{i}+\hat{k})\]
D) none of these
Correct Answer: C
Solution :
The required vector is along the vector \[\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{b})=(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{a}-(\overrightarrow{a}.\overrightarrow{a})\overrightarrow{b}\] \[=-(\hat{i}-\hat{j})-2(\hat{i}+2\hat{j})\] \[=-3\hat{i}-3\hat{j}\] Hence, required vector are given by \[\pm \frac{(-3\hat{i}-3j)}{\sqrt{9+9}}=\pm \frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\]
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