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

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}

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

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

$=1-1+1=1$