Question

Given that $\overset{\rightarrow}{A} + \overset{\rightarrow}{B} + \overset{\rightarrow}{C}$= 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

• A. 30⁰, 60⁰, 90⁰
• B. 45⁰, 45⁰, 90⁰
• C. 45⁰, 60⁰, 900⁰
• D. 90⁰, 135⁰, 135⁰

Answer 1

Answer: (D)

90⁰, 135⁰, 135⁰

Answer 2

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. i.e. the triangle should be right angled triangle

Angle between A and B, α = 90⁰

Angle between B and C, β = 135⁰

Angle between A and C, γ = 135⁰