Question

what is the angle between A vector and B vector if there resultant is r=√A^2+B^2
​

Answer 1

Answer:-

Given:

Resultant of two vectors A and B is R = √A² + B²

We know that,

Magnitude of Resultant (R) = √A² + B² + 2AB cos θ

where,

• A is magnitude of first vector
• B is Magnitude of second vector
• θ is the angle between them.

So,

⟶ √A² + B² = √A² + B² + 2AB cos θ

Squaring both sides we get,

⟶ (√A² + B²)² = (√A² + B² + 2AB cos θ)²

⟶ A² + B² = A² + B² + 2AB cos θ

⟶ A² + B² - A² - B² = 2AB cos θ

⟶ 0/2AB = cos θ

⟶ 0 = cos θ

⟶ cos 90° = cos θ

⟶ 90° = θ

∴ The angle between the vectors is 90°.