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Question

If a,b and c are vectors such that ab=0 and a+b=c, then

A
|a|2+|b|2=|c|2
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B
|b|+|c|=|a|
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C
|a|2+|c|2=|b|2
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D
|b|2+|c|2=|a|2
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Solution

The correct option is A |a|2+|b|2=|c|2
Given : ab=0
a+b=c
Squaring both sides,
(a+b)2=c2
(a+b)(a+b)=|c|2
aa+ab+ba+bb=|c|2
|a|2+0+0+|b|2=|c|2
|a|2+|b|2=|c|2

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