Vector has a magnitude of 11.0 and points in the positive y direction. A second vector, , has a magnitude of 13.5 and points at an angle of 44.0° below the x axis. Which vector has: (a) the greater x component, and (b) the greater y component?

(a) Vector 2 (13.5 units) has greater x-component

(b) Vector 1 (11 units) has greater x-component

Explanation:

Let the two vectors be "V₁" and "V₂". with magnitudes:

V₁ = 11 units

V₂ = 13.5 units

angles from x-axis:

θ₁ = 90°

θ₂ = 44°

So, the x-components of each will be:

V₁ₓ = V₁Cos θ₁ = (11)Cos (90°) = 0 units

V₂ₓ = V₁Cos θ₂ = (13.5)Cos (44°) = 9.71 units

(a)

Vector 2 (13.5 units) has greater x-component

(b)

So, the x-components of each will be:

V₁y = V₁Sin θ₁ = (11)Sin (90°) = 11 units

V₂y = V₁Sin θ₂ = (13.5)Sin (44°) = 9.37 units

Vector 1 (11 units) has greater x-component

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