Question

Two vectors ⃗

and ⃗
are shown in the figure. Vector ⃗
has a magnitude of =24.5
and an angle of =33.5∘.
Vector ⃗
has a magnitude of =46.9
and an angle of =57.5∘.
The figure is not to scale.

Express each vector in the figure using
unit vector notation,

⃗ =+

⃗ =+

where ,
,
,
and
are the calculated values of the
‑ and
‑components of vectors ⃗
and ⃗ ,
respectively.

A x y coordinate system with the positive x axis pointing horizontally to the right and the positive y axis pointing vertically upwards. Vector A extends from the origin into the first quadrant, has length r subscript A, and makes an angle theta subscript a with the positive x axis. Vector B extends from the origin into the third quadrant, has length r subscript b, and makes an angle theta subscript b with the negative x axis.

Answer 1

Step-by-step explanation:

To express each vector in the figure using unit vector notation, we can use the following equations:

⃗ =

⃗ =

where is the x-component of the vector and is the y-component of the vector.

For vector :

x = 24.5cos(33.5) = 20.8

y = 24.5sin(33.5) = 14.2

So

⃗ =

For vector :

x = -46.9cos(57.5) = -31.8

y = -46.9sin(57.5) = -38.4

So

⃗ =

Note that the negative sign on the x-component of vector is due to the fact that it is in the third quadrant.

It is important to take into account that the angle provided on the question is in degrees, and in this case trigonometric functions are used to calculate the x and y component of the vector.