If the magnitude of resultant of two vectors of equal magnitudes is equal to the magnitude of either vectors ,then find the angle between the two vectors ? Explain with figure ?

Question

If the magnitude of resultant  of two vectors of equal magnitudes is equal to the magnitude of either vectors ,then find the angle between the two vectors ? Explain with figure ?

Answer

Answer

Answer

This is an important result to remember. Two vectors at 120 degree produce a vector equal to their magnitude. Let their magnitude be a,
Resultant = a =√ (a2+a2+2×a×a×cosθ) = a√(2+2cosθ) => cosθ =−21
=>θ = 120 degree

Answer

Solution

Given

The magnitude of two vectors is equal.

To Find

The angle between the two vectors.

Solution

Let's suppose that the two vectors are represented as vector A and vector B, as shown in the figure below.

![image.png](attachment:image.png)

The magnitude of both vectors is equal, which means that |A| = |B|.

Now let's assume that the angle between the two vectors is θ, as shown in the figure.

The resultant of two vectors is given by the formula:

|R| = √(|A|² + |B|² + 2|A||B|cosθ)

As per the given condition, |R| = |A|

Therefore, we can write:

|A| = √(|A|² + |B|² + 2|A||B|cosθ)

Squaring both sides, we get:

|A|² = |A|² + |B|² + 2|A||B|cosθ

Simplifying, we get:

|B|² = 2|A||B|cosθ

Dividing both sides by 2|A||B|, we get:

cosθ = |B| / (2|A|)

Substituting |A| = |B|, we get:

cosθ = 1 / 2

Therefore, θ = 60°

Answer

The angle between the two vectors is 60 degrees.

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