Question

11- When the angle between two vectors of equal magnitude is 2T /3, then prove that the magni
tude of the resultant is equal to either.​

Answer 1

What is the angle between two vectors of equal magnitude when the magnitude of their sum is the same as the magnitude of each vector?

What is the best way to expand your professional network?

With Lunchclub, we have created a way to network over video both locally and globally. Previously, I have built networks over the

If the length of a⃗ , b⃗ and a⃗ +b⃗ are the same, we must have:

|a⃗ +b⃗ |2=|a⃗ |2

This means:

(a⃗ +b⃗ )⋅(a⃗ +b⃗ )=|a⃗ |2⇔|a⃗ |2+|b⃗ |2+2a⃗ ⋅b⃗ = |a⃗ |2

Since |a⃗ |2 and |b⃗ |2 are equal, this reduces to:

|a⃗ |2+2a⃗ ⋅b⃗ =0

By the law of cosines a⃗ ⋅b⃗ =|a⃗ ||b⃗ |cosθ , where θ is the angle between the vectors. Here, this reduces to a⃗ ⋅b⃗ =|a⃗ |2cosθ , and we get:

|a⃗ |2+2|a⃗ |2cosθ=0⇔|a⃗ |2(1+2cosθ)=0

Isolating, we get:

cosθ=−12

This has the solution of θ being equal to 120 degrees.