AP EAMCET202021 Sep 2020Morning ShiftMathematicsVector AlgebraActual

If ( a ) and ( b ) are unit vectors such that ( a + b ) is also a unit vector, then the angle between a and ( b ) is ____

Options

A(60^ )
B(90^ )
C(30^ )
D(120^ )

Correct answer

D. (120^ )

Step-by-step solution

For two vectors ( a ) and ( b ), it is given ( a + b ) is also unit vector, so ( aligned & | a + b |= 1 ( a + b )^2=1 & | a |^2+| b |^2+2 a b = l 1 + 1 +2 a b = 1 & a b =- 1 2 aligned ) Let angle between ( a ) and ( b ) is ( ) Then ( =- 1 2 =120^ ) Hence, option (d) is correct.

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