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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

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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Answer: 1

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

Explanation:

              \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]

           =1-1+1=1                               

                                                       

              

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