Question

I don’t understand how they got the answer can someone please do it in detail so I can understand

CHw01 Exercise 1.48 Part A Giv vectors A-400i +7.00, and E-5.00-2.00, firndthevetorproduct AxB Express your answer in terms of the unit vectors i, j, and k. Use the 'unlt vector button to denote unit vectors in your answer. en two

Answer 1

$We\,\,know\,\,for\,\,given\,\,two\,\,vector \\\,\,\overrightarrow{A}=x_1\hat{i}+y_1\hat{j}+z_1\hat{k} \,\, \,\,and\,\,\,\, \overrightarrow{B}=x_2\hat{i}+y_2\hat{j}+z_2\hat{k}$

$Vector\,\, product\,\,\overrightarrow{A}\times \overrightarrow{B}= \begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\ x_1&y_1 &z_1 \\ x_2&y_2 &z_2 \end{vmatrix}\\\\\\ Here\,\,given\,\,\,\, \overrightarrow{A}=4.00\hat{i}+7.00\hat{j} \,\, \,\,and\,\,\,\, \overrightarrow{B}=5.00\hat{i}-2.00\hat{j}\\\\ \therefore \,\,\overrightarrow{A}\times \overrightarrow{B}= \begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\ 4.00&7.00 &0 \\ 5.00&-2.00 &0 \end{vmatrix}$

  $\\ =\hat{i}(7.00\times0-0\times(-2.00)) \,-\,\hat{j}(4.00\times-0\times5.00)\,+\,\hat{k}(4.00\times(-2.00)-7.00\times5.00)\\\\ =-43.00\hat{k}$

$.\\\\\\\ [For\,\, any\,\, doubt\,\, please\,\, leave\,\, a \,\,comment]$