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2. Show that the vectors \vec a = \hat i - 2 \hat j + 3 \hat k, \vec b =- 2 \hat i + 3 \hat j -4\hat k \: \:and \: \: \vec c = \hat i -3 \hat j +5 \hat k  are coplanar.

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Given 

\vec a = \hat i - 2 \hat j + 3 \hat k, \vec b =- 2 \hat i + 3 \hat j -4\hat k \: \:and \: \: \vec c = \hat i -3 \hat j +5 \hat k

For coplanarity,

\left [ \vec a, \vec b,\vec c \right ]=0

So let's calculate the vector triple product of these three vectors,

\left [ \vec a, \vec b,\vec c \right ]=\begin{vmatrix} 1 &-2 &3 \\ -2& 3& -4\\ 1&-3 &5 \end{vmatrix}=1(15-12)+2(-10+4)+3(6-3)

3-12+9=0

Hence the three vectors are coplanar.

 

 

Posted by

Pankaj Sanodiya

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