Vector A ⃗ {\rm \vec A} points in the negative x x direction. Vector B ⃗ {\rm \vec B} points at an angle of 35.0 ∘ ^\circ above the positive x x axis. Vector C ⃗ {\rm \vec C} has a magnitude of 19m m and points in a direction 37.0 ∘ ^\circ below the positive x x axis.

Yes... and?

To determine the components (magnitude and direction) of vectors A⃗, B⃗, and C⃗, we can use trigonometry and the given information.

Let's start with vector A⃗, which points in the negative x direction. Since A⃗ is in the negative x direction, it means its x-component will be negative and the y-component will be zero. Therefore, the components of A⃗ can be written as:

A⃗ = (-|A⃗|, 0)

Moving on to vector B⃗, which points at an angle of 35.0∘ above the positive x-axis. We can use trigonometry to find the components of B⃗. The x-component can be calculated as:

Bx = |B⃗| * cos(angle)

Similarly, the y-component can be calculated as:

By = |B⃗| * sin(angle)

Substituting the given values, we have:

Bx = |B⃗| * cos(35.0∘)
By = |B⃗| * sin(35.0∘)

Lastly, let's find the components of vector C⃗, which has a magnitude of 19m and points 37.0∘ below the positive x-axis. Again, we can use trigonometry to calculate the components. The x-component can be written as:

Cx = |C⃗| * cos(angle)

The y-component can be written as:

Cy = -|C⃗| * sin(angle)

Note that the negative sign is used for Cy because C⃗ points below the positive x-axis. Substituting the given values, we get:

Cx = 19m * cos(37.0∘)
Cy = -19m * sin(37.0∘)

Therefore, the components for each vector A⃗, B⃗, and C⃗ can be calculated using trigonometry and the given information.