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  4. Given that vecA+ vecB+ vecC=0 out of three vectors two are equal in magnitude and the magnitude of third vector is √2 times that of either of the two having equal magnitude. Then the angles between vectors are given by

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Q. Given that $\vec{A}+\vec{B}+\vec{C}=0$ out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between vectors are given by

Motion in a Plane

Solution:

image
From polygon law, three vectors having summation zero should form a closed polygon (Triangle). Since the two vectors are having same magnitude and the third vector is $\sqrt{2}$ times that of either of two having equal magnitude.
That is, the triangle should be right angled triangle
Angle between $A$ and $B, \alpha=90^{\circ}$
Angle between $B$ and $C, \beta=135^{\circ}$
Angle between $A$ and $C, \gamma=135^{\circ}$