For which angle between two equal vectors vecA and vecB will the magnitude of the sum of two vectors be equal to the magnitude of each vector?

Question

For which angle between two equal vectors vecA and vecB will the magnitude of the sum of two vectors be equal to the magnitude of each vector? (A) θ=60° (B) θ=120° (C) θ=0° (D) θ=90°

Tardigrade Admin · Accepted Answer

| vecA+ vecB|=√A2+B2+2 A B cos 120° (θ=120°) =√A2+B2+ textnot 2 A B((-1/ textnot 2))( cos 120°=-(1/2)) =√A2+B2-A(A)=√B2=B (∴ A=B)

Q. For which angle between two equal vectors $A$ and $B$ will the magnitude of the sum of two vectors be equal to the magnitude of each vector?

$θ = 6 0^{\circ}$

$θ = 12 0^{\circ}$

$θ = 0^{\circ}$

$θ = 9 0^{\circ}$

$∣ A + B ∣ = A^{2} + B^{2} + 2 A B cos 12 0^{\circ}$
$(θ = 12 0^{\circ})$
$= A^{2} + B^{2} + not 2 A B (\frac{- 1}{not 2}) (cos 12 0^{\circ} = - \frac{1}{2})$
$= A^{2} + B^{2} - A (A) = B^{2} = B$
$(∴ A = B)$

Q. For which angle between two equal vectors A and B will the magnitude of the sum of two vectors be equal to the magnitude of each vector?

θ=60∘

θ=120∘

θ=0∘

θ=90∘