Question

if the resultant of two vector of equal magnitude 10 each is also 10 thennfind the angle between the two vector ? what is the angle the resultant makes w.r.t the vector added ,?

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Answer 1

Explanation:

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.