1.

Let a and b be unit vectors inclined at an angle 2alpha(0lealphalepi) each other, then (a+b) lt 1, if

Answer»

`ALPHA=(pi)/(2)`
`alphalt(pi)/(3)`
`alphagt(2pi)/(3)`
`(pi)/(3)ltalphalt(2pi)/(3)`

Solution :Given , `(a+b)lt 1`
` IMPLIES SQRT(1+12cos 2 alpha )lt 1`
` implies sqrt(2(1+cos 2 alpha ))lt 1`
`implies sqrt(4 cos^(2) alpha )lt 1`
`implies | cosalpha |lt (1)/(2)`
`implies (pi)/(3)lt alpha lt (2pi)/(3) [ :'0 le alpha le pi ]`


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