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  • If vector a b c are unit vectors such that , find the value of .

Q13  If  \vec a , \vec b , \vec c  are unit vectors such that \vec a + \vec b + \vec c = \vec 0, find the value of \vec a . \vec b + \vec b. \vec c + \vec c . \vec a 
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\vec a , \vec b , \vec c  are unit vectors    \Rightarrow |\vec a|=|\vec b|=|\vec c|=1

 and \vec a + \vec b + \vec c = \vec 0

and we need to find the value of \vec a . \vec b + \vec b. \vec c + \vec c . \vec a

(\vec a + \vec b + \vec c)^2 = \vec 0

\vec a^2 + \vec b^2 + \vec c ^2+2(\vec a . \vec b + \vec b. \vec c + \vec c . \vec a)=0

|\vec a|^2 + |\vec b|^2 + |\vec c |^2+2(\vec a . \vec b + \vec b. \vec c + \vec c . \vec a)=0

1+1+1+2(\vec a . \vec b + \vec b. \vec c + \vec c . \vec a)=0

\vec a . \vec b + \vec b. \vec c + \vec c . \vec a=\frac{-3}{2}

Answer- the value of \vec a . \vec b + \vec b. \vec c + \vec c . \vec a is \frac{-3}{2}

Posted by

Pankaj Sanodiya

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