Question

F1=6N,F2=8 making an angle of 45 find magn.. and direction​

Answer 1

Answer :

◈ Angle b/w F₁ and F₂ = 45°

We have to find magnitude and direction of the resultant vector$.$

◈ Magnitude of resultant vector :

➝ F² = F₁² + F₂² + 2F₁F₂cosΦ

➝ F² = 6² + 8² + 2(6)(8)cos45°

➝ F² = 36 + 64 + 96/√2

➝ F² = 100 + 68.08

➝ F = √168.08

➝ F ≈ 13N

◈ Direction of resultant vector :

➝ tanβ = F₁sinΦ/F₂+F₁cosΦ

➝ tanβ = 6sin45°/8+6cos45°

➝ tanβ = (6/√2)/8+(6/√2)

➝ tanβ = 3√2/8+3√2

➝ tanβ = 4.25/12.25

➝ tanβ = 0.35

➝ β = tanˉ¹(0.35)

See the attachment for better understanding.