1.

If a and b are unit vectors, then the greatest value of |a+b|+|a-b| is

Answer»

2
4
`2sqrt2`
`sqrt2`

Solution :LET `theta` be an ANGLE between UNIT vectors a and b. Then, `a.b =COS theta`
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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