Question

two equal vectors are along adjacent sides of a parallelogram and one of the diagonals root 3 times of the other then angle between vectors is

Answer 1

angle between vectors is π/3.

It has given that two equal vectors are along adjacent sides of a parallelogram and one of the diagonals √3 times of the other.

we have to find the angle between vectors.

let two vectors v and w are sides of parallelogram as shown in figure.

so two diagonals are v - w and v + w

now, |v + w| = √3|v - w|

squaring both sides we get,

⇒(|v + w|)² = 3(|v - w|)²

⇒v² + w² + 2vwcosθ = 3(v² + w² - 2vwcosθ)

⇒v² + w² + 2vwcosθ = 3v² + 3w² - 6vwcosθ

⇒8vwcosθ = 2v² + 2w²

here a/c to question, v = w

so, 8v² cosθ = 2v² + 2v² = 4v²

⇒cosθ = 1/2 = cosπ/3

⇒θ = π/3

therefore, angle between vectors is π/3.