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Question

If |¯x|=|¯y|=|¯x+¯y|=1 then |¯x¯y|= __________

A
3
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B
3
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C
2
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D
2
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Solution

The correct option is D 3
|x|=x and |y|=y
And,x=y=1
|x+y|2=1
x2+y2+2xycosθ=1
2+2cosθ=1
cosθ=12
Now,
|xy|2=x2+y22xycosθ
|xy|22cosθ=2+1=3
|xy|=3

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