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  • The volume of parallelopiped whose three coterminous edges are along vectors <img alt="\hat{\hat{i}}+\hat{j}-\hat{k}, 2 \hat{i}+2 \hat{j}-\hat{k}, 17 \hat{i}+7 \hat{j}-6 \hat{k}" src="https://

The volume of parallelopiped whose three coterminous edges are along vectors \hat{\hat{i}}+\hat{j}-\hat{k}, 2 \hat{i}+2 \hat{j}-\hat{k}, 17 \hat{i}+7 \hat{j}-6 \hat{k} is

Option: 1

5(unit)^{3}


Option: 2

10(unit)^{3}


Option: 3

15(unit)^{3}


Option: 4

20(unit)^{3}


Answers (1)

best_answer

As we learned

Volume of parallelopiped -

V = \left [ \vec{a}\;\vec{b}\; \vec{c}\right ]

Volume =\left | \left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ] \right |= \begin{Vmatrix} a_{1} &a_{2} &a_{3} \\ b_{1}& b_{2} & b_{3}\\ c_{1}& c_{2} & c_{3} \end{Vmatrix}= \begin{Vmatrix} 1 & 1 &-1 \\ 2& 2 &-1 \\ 17& 7 & -6 \end{Vmatrix}=10

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