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  • Position vectors of vertices of tetrahedron are  <img alt="\vec{0},2\hat{i},\hat{j},-\hat{k}" src="https://learn.careers360.com/latex-image/?%5Cvec%7B0%7D%2C2%5Chat%7Bi%7D%2C%5Chat%7Bj%7D

Position vectors of vertices of tetrahedron are  \vec{0},2\hat{i},\hat{j},-\hat{k} then its volume is 

Option: 1

\frac{5}{3} cubic unit

 

 


Option: 2

\frac{1}{3} cubic unit


Option: 3

\frac{2}{3}cubic unit


Option: 4

2 cubic units


Answers (1)

best_answer

As we learn

Volume of tetrahedron -

\frac{1}{6}\left [ \vec{a} \vec{b}\vec{c}\right ]

- wherein

The vertices of tetrahedron are  \vec{o}, \vec{a}, \vec{b}, \vec{c} .

 

 Volume =\left | \frac{1}{6}\left [ 2\hat{i}\ \hat{j}-\hat{k} \right ] \right |

=\left | \frac{1}{6}\left \{ 2\hat{i}\cdot \left \{ \hat{j}*-\hat{k} \right \} \right \}\right |=\left | \frac{1}{6}(-2) \right |=\frac{1}{3}

Posted by

Gautam harsolia

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