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Need solution for RD sharma maths class 12 chapter 24 vector or cross product Exercises Multiple choice questions question 14 maths textbook solution

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Given: \begin{aligned} &\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{k} \cdot(\hat{i} \times \hat{j}) \\ & \end{aligned}

Hint: You must know about the vector product of orthonormal triad of unit vectors


              \begin{aligned} &\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{k} \cdot(\hat{i} \times \hat{j}) \\ & \\ & \end{aligned}                  

           =\hat{i} \cdot(\hat{i})+\hat{j} \cdot(-\hat{j})+\hat{k} \cdot(\hat{k})                                                           {\left[\begin{array}{l} \because \hat{j} \times \hat{k}=\hat{i} \\ \hat{i} \times \hat{k}=-\hat{j} \\ \hat{i} \times \hat{j}=\hat{k} \end{array}\right]}

           =|\hat{i}|^{2}=|\hat{j}|^{2}+|\hat{k}|^{2}                                                                            \left[\begin{array}{l} \because|\hat{i}|^{2}=1 \\ |\hat{j}|^{2}=1 \\ |\hat{k}|^{2}=1 \end{array}\right]




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