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  4. Vectors A and B have equal magnitude. In addition, the magnitude of their resultant is also equal to the magnitude of either of them. Then A and B are at an angle of

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Q. Vectors A and B have equal magnitude. In addition, the magnitude of their resultant is also equal to the magnitude of either of them. Then A and B are at an angle of

KCETKCET 1993Motion in a Plane

Solution:

It is observed graphically that for $| \overrightarrow{A} | = |\overrightarrow{B} | = | \overrightarrow{R} |$ $\theta$ has to be $120^\circ$ Allter Using $R^2 = A^2 + B^2 + 2 \, AB \, cos \, \theta$ where R = B = A, we get $ A^2 = A^2 + A^2 + 2 \, A^2 \, cos \, \theta $ i.e. $cos \, \theta = - \frac{1}{2} $ i.e. $\theta = 120^0$

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