A) \[\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]
B) \[\frac{1}{\sqrt{5}}(2\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]
C) \[\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{k}})\]
D) none of these
Correct Answer: A
Solution :
The required vector is along the vector \[\overset{\to }{\mathop{\mathbf{a}}}\,\times (\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)=(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)\overset{\to }{\mathop{\mathbf{a}}}\,-(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,)\overset{\to }{\mathop{\mathbf{a}}}\,\] \[=-(\widehat{\mathbf{i}}-\widehat{\mathbf{j}})-2(\widehat{\mathbf{i}}+2\widehat{\mathbf{j}})\] \[=-3\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}\] Hence, required vector are given by \[\pm \frac{(-3\widehat{\mathbf{i}}-3\widehat{\mathbf{j}})}{\sqrt{9+9}}=\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]
You need to login to perform this action.
You will be redirected in
3 sec
