Question

What should be the angle between two vectors of equal magnitude such that the resultant of them also has the same magnitude as of either?

Answer 1

Answer:

45 degree I think soo..may be it is correct

Answer 2

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Two vectors having same magniude are inclined at angle Φ such that the resultant of them also has the same magnitude as of either vector.

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find angle between two vectors (Φ).

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

➠ Let two vectors A and B having equal magnitude (magnitude = x) are inclined at angle Φ. By triangle law or parallelogram law of vector addition, the magnitude of resultant vector R is given by

$\dag\:\underline{\boxed{\bf{\blue{R=\sqrt{A^2+B^2+2AB\cos\Phi}}}}}$

ATQ, R = A = B = x

$:\implies\sf\:x=\sqrt{x^2+x^2+2(x)(x)\cos\Phi}$

$:\implies\sf\:x^2=2x^2+2x^2\cos\Phi$

$:\implies\sf\:-x^2=2x^2\cos\Phi$

$:\implies\sf\:\cos\Phi=-\dfrac{x^2}{2x^2}$

$:\implies\sf\:\Phi=\cos^{-1}-\dfrac{1}{2}$

$:\implies\underline{\boxed{\bf{\purple{\Phi=120^{\circ}}}}}\:\orange{\bigstar}$