Question

A square + b square + 2 a b cos theta

Answer 1

Answer:

a correction in question...,

R square = a square+ b square + 2ab cos theta .

Explanation:

Given,

R² = a² + b² + 2ab cosθ

And |a| = |b|

so, R² = a² + b² + 2ab cosθ

⇒R² = |a|² + |b|² + 2|a||b| cosθ

⇒R² = |a|² + |a|² + 2|a|² cosθ [ ∵ |a| = |b| ]

⇒R² = 2|a|²(1 + cosθ)

⇒R² = 2|a|² × 2cos²θ/2 [ ∵(1 + cosx) = 2sin²x/2 ]

⇒R² = 4|a|²cos²θ/2

Taking square root both sides,

⇒R = 2|a|cosθ/2

Hence, magnitude of R equal to 2|a|cosθ/2.

Hope it helps you...