Question

if magnitude of two vectors are equal and there resultant is also equal to one of them.Then the angle with two vectors is​

Answer 1

Answer:

suppose ,two vector to be added have a equal magnitude then if resultant has also same magnitude ,the thre vectors (two to be added and one resultant ) will form a equilateral triangle .

Explanation:

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Answer 2

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

|a⃗ +b⃗ |2=|a⃗ |2|a→+b→|2=|a→|2

This means:

(a⃗ +b⃗ )⋅(a⃗ +b⃗ )=|a⃗ |2⇔|a⃗ |2+|b⃗ |2+2a⃗ ⋅b⃗ =(a→+b→)⋅(a→+b→)=|a→|2⇔|a→|2+|b→|2+2a→⋅b→= |a⃗ |2|a→|2

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

|a⃗ |2+2a⃗ ⋅b⃗ =0|a→|2+2a→⋅b→=0

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

Isolating, we get:

cosθ=−12cosθ=−12

θθ being equal to 120 degrees.