Question

Solve without using determinant form A.B×C= (Axi+Ayj+Azk). (Bxi+Byj+Bzk)× (Cxi+Cyj+Czk)

Answer 1

$B\times C=\begin{bmatrix} \hat{i}&\hat{j}&\hat{k} \\B_x&B_y&B_z \\ C_x&C_y&C_z \end{bmatrix}$

$$B\times C=\hat{i}(B_yC_z-B_zC_y)-\hat{j}(B_xC_z-B_zC_x)+\hat{k}(B_xC_y-B_yC_x)$$

$$A.(B\times C)=(A_x\hat{i}+\hat{j}A_y+\hat{k}A_z).(\hat{i}(B_yC_z-B_zC_y)-\hat{j}(B_xC_z-B_zC_x)+\hat{k}(B_xC_y-B_yC_x))$$

$$A.(B\times C)=A_x(B_yC_z-B_zC_y)-A_y(B_xC_z-B_zC_x)+A_z(B_xC_y-B_yC_x)$$