If the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vectors, then the angle between two vectors is a. 125° b. 130° c. 110° d. 120°

By Shivank Goel|Updated : August 12th, 2022

Given, that the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vector.

We have to find the angle between two vectors.

Let A and B be two given vectors.

Let R be the resultant vector

According to the question,

|A| = |B| = |R| = X

The magnitude of the vectors is given by

R = √(A2+B2+2ABcosθ)

Now, X = √(X2+X2+2X2cosθ)

X2 = 2X2 + 2X2cosθ

2X2cosθ = X2 - 2X2

2X2cosθ = -X2

2cosθ = -1

cosθ = -1/2

θ = cos⁻1(-1/2)

θ = 120°

Therefore, the angle between the vectors is 120°

Summary:

If the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vector, then the angle between the two vectors is

  1. 125°

  2. 130°

  3. 110°

  4. 120°

If the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vector, then the angle between the two vectors is 120°.

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