Question

the magnitude of the resultant of two vectors of equal magnitude become √3 times when the direction of either vector is changed. what's the angle between the two vectors?​

Answer 1

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Answer 2

Answer:

120°

Explanation:

let the initial resultant magnitude be V and final be $\sqrt{3}$V

both vectors have equal magnitude as given.i.e.a1=a2=a

case I: when acting in the same direction

V=$\sqrt{a1^2+a2^2+2a1a2cos\alpha }$

V=$\sqrt{2a^2+2a^2cos\alpha }$    (1)

case II: when acting in the opposite direction

$\sqrt{3}$V=$\sqrt{a1^2+a2^2-2a1a2cos\alpha }$    

$\sqrt{3}$V=$\sqrt{2a^2-2a^2cos\alpha }$        (2)

from equations 1 and 2 we get,

3$a^{2}$+$3a^{2} cos\alpha =a^{2} -a^{2} cos\alpha$

$4a^{2} cos\alpha =-2a^{2}$

$cos\alpha =-1/2$

$\alpha$=120°