Question

if the resultant of two vectors is equal to sum of their magnitude find the angle between the vectors

Answer 1

Angle between the vectors is 0°

Suppose two forces F are acting on a block in same direction with 0° angle between them, then resultant force on block is F + F = 2F

E.g. When a car is pushed by people in the same direction (θ = 0°) then the resultant force acting on car is Sum of forces applied by people on the car.
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If you want mathematical answer then,

R = sqrt(a² + b² + 2abCosθ)

According to question R = a + b

(a + b) = sqrt(a² + b² + 2abCosθ)

(a + b)²= a² + b² + 2abCosθ

a² + b² + 2ab = a² + b² + 2abCosθ

2ab = 2abCosθ

Cosθ = 1

θ = 0°