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Question

¯a & ¯b are two non-collinear vectors then find the value of ¯a|¯a|2¯b¯b22 is equal to

A
¯a¯bab
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B
(¯a¯bab)3
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C
(¯a¯bab)2
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D
(¯a¯b)2
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Solution

The correct option is C (¯a¯bab)2
{¯a|¯a|2¯b¯b|2}2=|a|2|¯a|4+|¯b|2|b|42ab|a|2|¯b2
=1|a|2+11¯b|22ab|a|2|¯b|2=|a|2+|b|2˙2ab|a|2|¯b2
=(ab)2|¯a|2|¯b|2=(abab)2
option C is correct.

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