Question

The displacement vector has scalar components of Ax = 80.0 m and Ay = 60.0 m. The displacement vector has a scalar component
of Bx = 60.0 m and a magnitude of B = 75.0 m. The displacement vector has a magnitude of C = 100.0 m and is directed at an angle of
36.9° above the +x axis. Determine which two of these vectors are equal.

Answer 1

Answer:

Vectors A and C are equal

Explanation:

If we have a certain vector $\displaystyle \overrightarrow{A}$, the components of the vector $\displaystyle \mathrm {A_x\;and\;A_y}$ are  given by:
$A_x = Acos\theta\\A_y=Asin\theta$

where
$\textrm { \theta is the angle formed by the vector on the x-axis}$

For vector A, we have Ax = 80m and Ay=60m

For vector C we have
Cx = |C| cosθ = 100 cos(36.9) ≈ 100 x 0.8 = 80m
Cy = |C| sinθ = C sin(36.9) ≈ 100 x 0.6 = 60m

So A and C are equal

We can eliminate B since Bx = 60 and Ax=80 so they cannot be equal