If →a,→b,→c are non-zero, non-coplanar vectors then {→a×(→b+→c)}×{→b×(→c−→a)} is collinear with the vector
A
→a+→b+→c
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B
→a−→b+→c
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C
→a+→b−→c
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D
→a−→b−→c
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Solution
The correct option is C→a−→b−→c ¯¯¯p×(¯¯¯qׯ¯¯r)=(¯¯¯p.¯¯¯r)¯¯¯q−(¯¯¯p.¯¯¯q)¯¯¯r
Thus, we have the given expression equal to ¯¯¯a×(¯¯b+¯¯c).(¯¯c−¯¯¯a)¯¯b−(¯¯¯a×(¯¯b+¯¯c).¯¯b)(¯¯c−¯¯¯a) =[¯¯¯a¯¯b¯¯c]¯¯b+[¯¯¯a¯¯b¯¯c](¯¯c−¯¯¯a) =−[¯¯¯a¯¯b¯¯c](¯¯¯a−¯¯b−¯¯c)