vector magnitude and angle

Question

A)Determine the magnitude of the sum of the three vectors V⃗ 1=8.0i^−9.0j^,V⃗ 2=i^+j^V→1=8.0i^−9.0j^,V→2=i^+j^, and V⃗ 3=−2.0i^+5.0j^V→3=−2.0i^+5.0j^.

b)Determine the angle (in degrees) of the sum of the three vectors V⃗ 1=8.0i^−9.0j^,V⃗ 2=i^+j^V→1=8.0i^−9.0j^,V→2=i^+j^, and V⃗ 3=−2.0i^+5.0j^V→3=−2.0i^+5.0j^.

Answer 1

V₁ = 8.0i - 9.0j

V₂ = 1.0i + 1.0j

V₃ = -2.0i + 5.0j

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V_T = 7.0i - 3.0j

The magnitude is determined using the Pythagorean Theorem = √(7² +(-3)²) = √(49+9) = √58 ≈ 7.6

The direction is determined using trig ratios: tan(θ) = opp/adj = -3/7 therefore θ = tan^-1(-3/7) ≈ -23°