Two vectors of same magnitude act at a point. | vedclass

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(C) Let the magnitude of the two vectors be $A$ and $B$. Given that they have the same magnitude,let $A = B = x$.The resultant magnitude $R$ is given

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$90$

Vedclass · Answer

(C) Let the magnitude of the two vectors be $A$ and $B$. Given that they have the same magnitude,let $A = B = x$.The resultant magnitude $R$ is given by the formula $R^2 = A^2 + B^2 + 2AB \cos 	heta$,where $	heta$ is the angle between the vectors.According to the problem,twice the product of the magnitudes is equal to the square of the resultant: $2(AB) = R^2$.Substituting $A = x$ and $B = x$,we get $2(x \cdot x) = x^2 + x^2 + 2(x \cdot x) \cos 	heta$.This simplifies to $2x^2 = 2x^2 + 2x^2 \cos 	heta$.Subtracting $2x^2$ from both sides,we get $0 = 2x^2 \cos 	heta$.Since $x 
eq 0$,we must have $\cos 	heta = 0$.Therefore,$	heta = 90^{\circ}$.

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is (in $^{\circ}$)

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