First slide

Scalars and Vectors

Question

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

Easy

A

$30^{\circ}, 60^{\circ}, 90^{\circ}$
B

$45^{\circ}, 45^{\circ}, 90^{\circ}$
C

$45^{\circ}, 60^{\circ}, 90^{\circ}$
D

$90^{\circ}, 135^{\circ}, 135^{\circ}$

Solution

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, $α = 90^{\circ}$
Angle between B and C, $β = 135^{\circ}$
Angle between A and C, $γ = 135^{\circ}$

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