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Question

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
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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

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