Consider the vectors v⇀ = ⟨1, 6⟩ and w⇀ = ⟨0, –4⟩. What are the component form, magnitude, and direction of v⇀ + w⇀? Round to the nearest tenth of a unit.

Answer 1

component form: the ordered pair that describes the changes in the x- and y-values

1. if you want to add two vectors, you should add their respective components
2. v⇀ + w⇀ = ⟨1, 6⟩ + ⟨0, -4⟩ = ⟨1 + 0, 6 + -4⟩ = ⟨1, 2⟩

magnitude: the distance between the initial point and the ending point of the summed vector

1. initial point: implied to be (0, 0)
2. ending point: ⟨1, 2⟩ (as shown above)
3. distance formula: √((x₂ - x₁)² + (y₂ - y₁)²) = √((1 - 0)² + (2 - 0)²) = √(1 + 4) = √5 ≈ 2.2

direction: the counterclockwise angle of rotation θ that the vector points at with respect to the positive x-axis

1. tan(θ) = y-component / x-component = 2 / 1 = 2
2. θ = arctan(2) ≈ 63.4º