If | vector A -vec B| = |vec A| = | vecB| , the angle between vector A and vector B is

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Solution

we know that |A-B|=|A+(-B)|=square root(A^2+B^2-ABcos(theta))
where A and B are magitudes of vectors A and B.
it is said that
it is said that this is equal to either the magnitude of each of these A and B
so it is obvious that A=B
so |A-B|=square root(A^2+A^2+2AAcos(theta)|=|A|^2
squaring on both sides
2A^2+2A^2cos(theta)=A^2
2A^2(1+cos(theta))=A^2
2(1+cos(theta))=1
1+cos(theta)=1/2
cos(theta)=-1/2
cos(theta)=cos120=1/2
theta=120
so the angle is 120 in degree

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