Question

If two vectors are unit vectors then the third vector joining them them will also be unit vector...
How ???

Answer 1

Let the vectors be  P and Q, with an angle Ф between them.
Let the resultant vector be R.
magnitude of all of them is = 1 unit.
Vector addition law:
R² = P² + Q² + 2 P Q cosФ
1 = 1 + 1 + 2 cos Ф

so cos Ф = -1/2    ==>   P & Q vectors are inclined at  120°
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If vector R joins the end points of P & Q vectors, then:

R² = P² + Q² - 2 P Q Cos Ф
1 = 1 + 1 - 2 cos Ф
cos Ф = 1/2   => the two vectors are inclined at 60°