# Two vectors of equal magnitude have a resultant equal to either of them in magnitude. The angle between them is:

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.

• 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. Aug 2 at 10:27

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 $$\sqrt{2}|\vec{A}|=\sqrt{2}|\vec{B}| \neq |\vec{A}|=|\vec{B}|$$
• @SrijanM.T Yes, of course only one case when the angle between the vectors of equal magnitude is $120°$ Aug 2 at 9:22