Question

two vector having equal magnitude of 5 units, have an angle of 60° between them. find the magnitude of their resultant vector and it's angle from one of the vector.​

Answer 1

Given :

Two vectors having equal magnitude of 5 units are inclined at an angle of 60°.

To Find :

Magnitude of resultant vector and it's angle from one of the vector.

Solution :

Let two vectors A and B of equal magnitudes are inclined at an angle θ$.$

As per parallelogram law of vector addition, magnitude of resultant vector R of two vectors A and B inclined at angle θ is given by

• R² = A² + B² + 2AB cosθ

By substituting the given values;

➠ R² = A² + B² + 2AB cosθ

➠ R² = 5² + 5² + 2(5)(5) cos60°

➠ R² = 25 + 25 + (50 × √3/2)

➠ R² = 50 + 25√3

➠ R² = 50 + 43.25

➠ R² = 93.25

➠ R = √93.25

➠ R = 9.65 units

Since both vectors have equal magnitude, resultant vector will make angle of 30° with each vector.