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If a and b are unit vectors, then the greatest value of |a+b|+|a-b| is |
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Answer» 2 Now, `|a+b|^(2)=|a|^(2)+|b|^(2)+2a.b` `=1+1+2xx1xx1xxcos theta` `=2+2 cos theta=4 "cos"^(2) theta/2` `implies |a+b|=2 "cos" theta/2` and `|a-b|^(2)=|a|^(2)+|b|^(2)-2a.b` `=2-2 cos theta=2 (2 "SIN"^(2) theta/2)` `|a-b|=2"sin" theta/2` `:. |a+b|+|a-b|=2 ("cos" theta/2 +"sin"theta/2) le 2 sqrt(2)` |
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