Answer to Question #149208 in Classical Mechanics for David mark

Question

Given that vector A =5i-7j+3k and B=-4i+4j-8k,find (I)AxB(ii)BxA

Answer 1

Given,

$A =5\hat{i}-7\hat{j}+3\hat{k},$

$B=-4\hat{i}+4\hat{j}-8\hat{k}$

$A\times B = \begin{bmatrix} \hat{i} & \hat{j}& \hat{k}\\ 5 & -7 & 3\\ -4 & 4 & -8\\ \end{bmatrix}$

$=\hat{i}(56-12)-\hat{j}(-40+12)+\hat{k}(20-28)$

$=44\hat{i}+28\hat{j}-8\hat{k}$

$B\times A = \begin{bmatrix} \hat{i} & \hat{j}& \hat{k}\\ -4 & 4 & -8\\ 5 & -7 & 3\\ \end{bmatrix}$

$=\hat{i}(12-56)-\hat{j}(-12+40)+\hat{k}(28-20)$

$=-44\hat{i}-28\hat{j}+8\hat{k}$