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A tertrahedron has centroid   \hat i +2 \hat j + \hat k  with position vector \hat i -\hat j , 2 \hat i + \hat j , -3 \hat i + \hat k. 

Then fourth vector has position vector 

Option: 1

4 \hat i - 8 \hat j + 8 \hat k


Option: 2

4 \hat i + 8 \hat j + 3 \hat k


Option: 3

4 \hat k


Option: 4

4 \hat i - 8 \hat j - 3 \hat k


Answers (1)

best_answer

As we have learned

Centroid of tetrahedron -

Position Vector of tetrahedron =\frac{1}{4}\left [ \vec{a}+ \vec{b}+\vec{c}+\vec{d}\right ]

- wherein

\vec{a}, \vec{b}, \vec{c}, \vec{d}are four vectors.

 

 

 

 \hat i +2 \hat j + \hat k = 1/4 (\hat i - \hat j + 2 \hat i + \hat j - \hat i + \hat k + \vec r )

\hat i +2 \hat j + \hat k = 1/4(\vec k + \vec r ) \Rightarrow \vec r = 4 \hat i + 8 \hat j + 3 \hat k

 

 

 

 

Posted by

Anam Khan

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