a Let's begin with recalling how we should perform vector addition.
⟨ a,b ⟩ + ⟨ c,d ⟩ = ⟨ a+c,b+d ⟩
In our exercise we are given that Sydney parked her car and hiked along two paths described by the vectors ⟨ 2, 3⟩ and ⟨ 5,-1⟩ . To find what vector represents her hike along both paths, we need to add these two vectors.
Her hike along both paths can be represented by the vector ⟨ 7,2⟩ .
b In this part we are asked to evaluate how far Sydney is from her car. To do this, we need to evaluate the magnitude of a vector we found in the previous part. Having been given the component form of a vector ⟨ x_1,y_1 ⟩, we can find the magnitude by substituting (7, 2) and (0,0) into the Distance Formula.
