Question

If sum of two unit vectors is also a unit vector . Find the magnitude of their difference.

Answer 1

heya...........nyc to meet u once @sohan


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let two vectors are a,b then

resultant of sum = (a2 + b2 + 2abcos@)1/2 = 1               (given)

a = b = 1          (unit vector)

 1+1+2cos@ = 1

      cos@ = -1/2           .................1

now resultant of difference = magnitude (a-b)

R = (a2 + b2 - 2abcos@)1/2

a = b = 1 , cos@ = -1/2 so

R = [ 1+1+1]1/2 = √3

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tysm....................#kundan

Answer 2

Let  and B ate the given unit vectors and Ô is their resultant then

|Ô| = | Â + B |

$1 = \sqrt{ ({ Â}^{2} + {B}^{2} + 2 |Â| |B| \cos( \alpha )} \\ 1 = 1 + 1 + 2 \cos( \alpha ) = \ \textgreater \ \cos( \alpha ) = \frac{ -1 }{2} \\ | {A}^{ - \ \textgreater \ } - {B}^{ - \ \textgreater \ } | = \sqrt{ ({ Â}^{2} + {B}^{2} - 2 |Â| |B| \cos( \alpha )} \\ = \sqrt{1 + 1 - 2 \times 1 \times 1( \frac{ - 1}{2}) } = \sqrt{3}$