If →a,→b,→c are non-zero vectors such that |(→a×→b).→c|=|→a||→b||→c|, then |→a+→b+→c|2=
A
0
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B
1
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C
|→a|2+|→b|2+|→c|2
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D
−1
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Solution
The correct option is D|→a|2+|→b|2+|→c|2 ⎛⎜
⎜⎝a2¯¯¯a.¯¯b¯¯¯a.¯¯c¯¯b.¯¯¯ab2¯¯b.¯¯c¯¯c.¯¯¯a¯¯c.¯¯bc2⎞⎟
⎟⎠=(¯¯¯aׯ¯b.¯¯c)2 Thus, we get that all the dot products in the determinant are 0. And so, |¯¯¯a+¯¯b+¯¯c|2=|¯¯¯a|2+|¯¯b|2+|¯¯c|2