Question

The diagram shows three vectors.

Three vectors drawn on the x y plane. The first vector is 8 blocks long drawn in the positive x direction along the x axis and labeled P Subscript x Baseline.The second is drawn tail to tip method, is 6 blocks high, drawn north and labeled P Subscript y Baseline. The last is drawn from the tail of the first to the head of the second and labeled P. The angle between P and P Subscript x Baseline is labeled theta.
Which best describes a relationship among the vectors?



Vectors P and Py are components of vector Px.
Vectors Px and Py are components of vector P.

Answer 1

"Vectors Px and Py are components of vector P."

Reason: P is the resultant from the tail of Px to the head of Py, so P = Px + Py. Numerically P = sqrt(8^2 + 6^2) = 10 and θ = arctan(6/8) ≈ 36.9°. Also Px = P cosθ = 8 and Py = P sinθ = 6.