Find the volume of a cuboid whose edges are given by -3\hat{i}+7\hat{j}+5\hat{k},-5\hat{i}+7\hat{j}-3\hat{k}\: \: and\: \: \: 7\hat{i}-5\hat{j}-3\hat{k}.

 

 

 

 

 
 
 
 
 

Answers (1)

Given: \: a,b,c are edges of a cuboid.

Then, volume of cuboid, = \vec{a}\cdot \left ( \vec{b}\times \vec{c} \right )

Here, \vec{a}=-3\hat{i}+7\hat{j}+5\hat{k}

\vec{b}=-5\hat{i}+7\hat{j}-3\hat{k}

\vec{c}=7\hat{i}-5\hat{j}-3\hat{k}

Then, 

\vec{a}\left ( \bar{b}\times\bar{c} \right )= \begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\ -3 & 7 & 5\\ -5 & 7 & -3\\ 7 &-5 &-3 \end{vmatrix}

=-3(-21-15)-7(15+21)+5(25-49)

=-3\times (-36)-7\times36+5\times(-24)

=108-252-120\Rightarrow -264\: cubic \:units

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