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  • Let   <img alt="\vec a = \hat i + \hat j + \hat k , \vec b = \hat i - \hat j - \hat k , \vec c = 2 \hat i + \hat j - \hat k" src="https://learn.careers360.com/latex-image/?%5Cvec%20a%20%3

Let   \vec a = \hat i + \hat j + \hat k , \vec b = \hat i - \hat j - \hat k , \vec c = 2 \hat i + \hat j - \hat k   then a vector  in the place of \vec b \:and \: \vec c are perpendicular to \vec a  is 

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

As we have learned

Vector Triple Product -

\vec{a}\times \left ( \vec{b} \times \vec{c}\right ) is a vector perpendicular to the plane containing \vec{a}, \vec{b}, \vec{c}  are three vectors.

-

 

 Required vector can be either in direction of \vec a \times ( \vec b \times \vec c)   or in opposite direction 

\vec a \times (\vec b \times \vec c) =(\vec a \cdot \vec c) \vec b- (\vec a \cdot \vec b) \vec c = 

2 (\hat i - \hat j - \hat k) - (-1)(2 \hat i + \hat j - \hat k)= 4 \hat i - \hat j -3 \hat k

 

Posted by

Pankaj Sanodiya

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