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  • Let Then If c1 = 1 and c2 = 2, find c3 which makes coplanar

4 (a)   Let \vec a = \hat i + \hat j + \hat k , \vec b = \hat i \: \: and \: \: \vec c = c_1 \hat i + c_2 \hat j + c_3 \hat k  Then
             If c_1 = 1 and c_2 = 2  find c_3 which makes \vec a , \vec b , \vec c coplanar

Answers (1)

best_answer

Given

\\\vec a = \hat i + \hat j + \hat k ,\\ \vec b = \hat i \: \: and \: \: \\ \vec c = \hat i + 2 \hat j + c_3 \hat k

These will be coplanar when 

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

\begin{vmatrix} 1 &1 &1 \\ 1& 0& 0\\ 1&2 &c_3 \end{vmatrix}=1(0)-1(c_3)+1(2)=0

-c_3+2=0

c_3=2

Hence the value of c_3for which vectors will be coplanar is 2.

Posted by

Pankaj Sanodiya

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