Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 25, direction angle θ = 30°

1 answer

To find the component form of the vector, we can use the formula:

v = ⟨v_x, v_y⟩

where v_x is the horizontal component and v_y is the vertical component.

The magnitude of the vector is given as 25 and the direction angle θ is given as 30°. We can use trigonometry to find the horizontal and vertical components.

The horizontal component can be found using the formula:

v_x = v * cos(θ)

Substituting the given values:

v_x = 25 * cos(30°)

Using a calculator:

v_x ≈ 21.7

The vertical component can be found using the formula:

v_y = v * sin(θ)

Substituting the given values:

v_y = 25 * sin(30°)

Using a calculator:

v_y ≈ 12.5

Therefore, the component form of the vector is approximately ⟨21.7, 12.5⟩.