The magnitude of a vector is the length from the its initial point to its terminal point. Having been given the component form of a vector ⟨ x_1,y_1 ⟩, we can find the magnitude by substituting (x_1,y_1)=(4,-8) and (x_2,y_2)=( 0, 0) into the Distance Formula.
The direction of a vector can be expressed as the angle it forms with the horizontal axis if the initial point is placed at the origin. Let's graph d, its horizontal component, and its vertical component.
The direction of our vector will be the angle α. Note that α and θ add up to be a 360 ^(∘) angle. Therefore, we can find α by subtracting θ from 360 ^(∘).
α+ θ =360 ^(∘) ⇔ α= 360 ^(∘)- θ
We can find θ using trigonometry. The tangent of θ is equal to the ratio of the length of the opposite side divided by the length of the adjacent side.
Tangent=Opposite/Adjacent ⇒ tan θ = 84
To find θ we can use the inverse tangent ratio and solve with a calculator.
