Question

Two equal forces f and f makes an angle of 180 with each other the magnitude of their resultant is

Answer 1

Answer :

Two equal forces of F and F makes an angle of 18p° with each other.

We have to find magnitude of their resultant $.$

★ By triangle law or parallelogram law of vector addition, the magnitude of resultant R at two vectors A and B inclined to each other at angle θ is given by

• R² = A² + B² + 2AB cosθ

ATQ, A = B = F

Angle (θ) = 180°

By substituting the values, we get

➠ R² = F² + F² + 2(F)(F) cos180°

➠ R² = 2F² + 2F²(-1)

• cos180° = -1

➠ R² = 2F² - 2F²

➠ R² = 0

➠ R = 0

∴ Magnitude of their resultant is zero.

★ Additional Information :

• Null vector is a vector which has zero magnitude and an arbitrary direction.
• A negative vector of a given vector is a vector of some magnitude but acting in a direction opposite to that of the given vector.
• A vector whose initial point is fixed is called a localised vector.