If \vec{a}=2\hat{i}+3\hat{j}+\hat{k}, \vec{b}=\hat{i}-2\hat{j}+\hat{k} and \vec{c}= -3 \hat{i}+\hat{j}+2\hat{k}, find   [\vec{a},\vec{b},\vec{c}]

 

 

 

 
 
 
 
 

Answers (1)

Given : \vec{a}=2\hat{i}+3\hat{j}+\hat{k}

            \vec{b}=\hat{i}-2\hat{j}+\hat{k}

            \vec{c}=-3\hat{i}+\hat{j}+2\hat{k}

Now,  [\vec{a},\vec{b},\vec{c}]=[\vec{a}\cdot(\vec{b}\times \vec{c}) ]

                         =\begin{vmatrix} 2 &3 &1 \\ 1& -2 &1 \\ -3& 1 &2 \end{vmatrix}

                              =2(-4-1)-3(2+3)+1(1-6)

=2(-5)-3(5)+1(-5)

=-10-15-5

=-30

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