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Question

If a and b are unit vectors inclined at angle of 30o to each other, then which one of the following is correct?

A
a+b=2
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B
a+b>2
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C
a+b>1
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D
1<a+b<2
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Solution

The correct option is D 1<a+b<2
|a|=|b|=1
θ=30o
|a+b|2=|a|2+|b|2+2a,b
|a+b|2=1+1+2|a||b|cos30o
=2+2×32

|a+b|2=2+3
|a+b|=2+3
1<|a+b|<2

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