Question

Consider the vectors ⇀ v ⇀ = ⟨1, 6⟩ and ⇀w⇀ = ⟨0, −4⟩. What is the magnitude of ⇀v⇀ + ⇀w⇀ expressed to the nearest tenth of a unit?

A. 10.1
B. 6.1
C. 4.0
D. 2.2

Answer 1

To find the magnitude of the vector ⇀v⇀ + ⇀w⇀, we need to add the components of ⇀v⇀ and ⇀w⇀ and then calculate the magnitude of the resulting vector.

⇀v⇀ + ⇀w⇀ = ⟨1, 6⟩ + ⟨0, -4⟩ = ⟨1+0, 6+(-4)⟩ = ⟨1, 2⟩

The magnitude of a vector is calculated using the formula: magnitude = √(x² + y²), where x and y are the components of the vector.

For the vector ⟨1, 2⟩, the magnitude is:

magnitude = √(1² + 2²) = √(1 + 4) = √5 ≈ 2.2

Therefore, the magnitude of ⇀v⇀ + ⇀w⇀ is approximately 2.2.

The correct answer is D. 2.2.