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  • Volume of parallelopiped with its co terminus edges along vectors <img alt="\vec a , \vec b \: \: and \: \: \vec c" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%20a%20%2C%20%5Cv

Volume of parallelopiped with its co terminus edges along vectors \vec a , \vec b \: \: and \: \: \vec c  is 24 cubic units , then volume of tetrahedron having its vertices with position \vec 0 , \vec a + \vec b , \vec b + \vec c ,\vec c + \vec a willbe 

Option: 1

4


Option: 2

6


Option: 3

8


Option: 4

12


Answers (1)

best_answer

As we have learned

Properties of Scalar Triple Product -

\left [ \vec{a}+\vec{b}\:\:\vec{b} +\vec{c}\:\:\vec{c} +\vec{a} \right ]= 2\left [ \vec{a}\vec{b} \vec{c}\right ]

- wherein

\vec{a}, \vec{b}, \vec{c}are three vectors

 

 Given |[\vec a\; \; \vec b\; \; \vec c]|=24 

Required volume = |1/6[\vec a+ \vec b\; \; \vec b + \vec c\; \; \vec c+ \vec a]|=|1/3 [\vec a \; \vec b\; \vec c ]|= 8

 

 

 

 

 

 

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