Find the magnitude of each of the two vectors 𝐚 and 𝐛, having the same magnitude such that the angle between them is 60° and their scalar product is 92.

We know that for any two given vectors 𝐚 and 𝐛, 𝐚.𝐛 = |a||b|cosθ. It is also given that 𝐚 and 𝐛 are equal in magnitude. Hence, |a| = |b|. After substitution we get: 𝐚.𝐛 = |a||a|cos60° ⇒ 𝐚.𝐛 = |a|²cos60° ⇒ 92 = |a|² × 1/2 ⇒ |a|² = 184 ⇒ |a| = √184 = 2√46. As |a| = |b|, magnitude of 𝐚 and 𝐛 is equal to 2√46.