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The diagram shows vectors that are not perpendicular to one another.

Three vectors are drawn tail to tip method in the x y plane. Vector labeled E starts at the origin and is drawn in the northeast direction. The second vector is labeled F and drawn in the south southeast direction. The third is labeled G and drawn in the north northeast direction. X and Y components are drawn for each vector along the x and y axis.

The data table shows the magnitudes of the components of each displacement vector.

A 2 column table with 5 rows. The first column is labeled Component with entries E Subscript x Baseline, F Subscript x Baseline, G Subscript x Baseline, E Subscript y Baseline, F Subscript y Baseline, G Subscript y Baseline. The second column is labeled Magnitude in centimeters with entries 2, 4, 2, 2, 1, 3.

What is the angle of the resultant vector, rounded to the nearest tenth?

0.1°
10.0°
36.9°
41.1°

Answer :

Onyebuchinnajigo

The angle of the resultant vector, rounded to the nearest tenth is determined as 36.9⁰.

Magnitude of components vectors

The resultant vector of the three vectors can be determined from the magnitude of the components vectors.

     Ex   = 2

     Fx   = 4

     Gx  = 2

     Ey =   2

     Fy =   1

     Gy =  3

∑Vx = Ex + Fx + Gx  = 2 + 4 + 2 = 8

∑Vy = Ey + Fy + Gy = 2 + 1 + 3 = 6

Angle of the resultant vector

tanθ = Vy/Vx

tanθ = 6/8

tanθ = 0.75

θ = tan⁻¹(0.75)

θ =  36.9⁰

Thus, the angle of the resultant vector, rounded to the nearest tenth is determined as 36.9⁰.

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