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Let the two vectors be A and B.

|A|=|B| but not direction is equal is told in the Q. So , let us take two cases .

a) Direction is equal & b) Direction is not equal.

a) Let’s say both A and B vectors lie on the X axis. Then , so will their resultant. Therefore , angle by R between either of them is always = 0 degrees.

b) Let’s say A is pointing towards X axis and Y towards Y axis. Direction of resultant is between the two vectors.

Angle between R with either A or B is always = 45 degrees.

According to me , the question is. incomplete.

But from a solution online , what they have done is that :

$R^2 = A^2 + B^2 + 2(A)(B)cos \theta$

Since |A|=|B| , then we get $\theta$ = 120 degree from here.

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  • $\begingroup$ Maybe easier to visualize: when adding two vectors, you can make a triangle out of the vectors and the resultant vector. The question is essentially asking when this triangle is equilateral. $\endgroup$ Aug 2 at 10:27
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As you said, "b) Let’s say A is pointing towards X axis and Y towards Y axis. Direction of resultant is between the two vectors Angle between R with either A or B is always = 45 degrees".

Yes, the angle between resultant vector and either of the vectors will be $45°$ but the magnitude of Resultant vector in such a case will be $\sqrt{2}|\vec{A}|=\sqrt{2}|\vec{B}| \neq |\vec{A}|=|\vec{B}|$

When direction is same then the magnitude of resultant vector will be double of that of either of the vectors, therefore direction of the two vectors can't be same.

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  • $\begingroup$ Ok. I didn’t think that. $\endgroup$
    – S.M.T
    Aug 2 at 9:20
  • $\begingroup$ So , there is always just 1 case possible. $\endgroup$
    – S.M.T
    Aug 2 at 9:20
  • $\begingroup$ @SrijanM.T Yes, of course only one case when the angle between the vectors of equal magnitude is $120°$ $\endgroup$ Aug 2 at 9:22
  • $\begingroup$ Ok. Thanks a lot $\endgroup$
    – S.M.T
    Aug 2 at 9:23
  • $\begingroup$ Do we say either of the vectors A or B is equal to Vector of resultant or only magnitude ? $\endgroup$
    – S.M.T
    Aug 5 at 11:25

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