Question

Let a=⟨−7,3⟩a=⟨−7,3⟩ and b=⟨−2,−12⟩b=⟨−2,−12⟩, and c=a+bc=a+b. What is the magnitude and direction angle of cc?

a) ∣c∣=18; θ=135∘∣c∣=18; θ=135∘
b) ∣c∣=18; θ=225∘∣c∣=18; θ=225∘
c) ∣c∣=92; θ=135∘∣c∣=92​; θ=135∘
d) ∣c∣=92; θ=225∘∣c∣=92​; θ=225∘

Answer 1

To find the magnitude and direction angle of vector c = a + b = (-7,3) + (-2,-12), we calculate ∣c∣ = 9*sqrt(2) and θ = 45°.

Step-by-step explanation:

To find the magnitude and direction angle of vector c, we need to calculate c using the given vectors a and b:

c = a + b = (-7,3) + (-2,-12) = (-9,-9)

The magnitude of vector c is found using the formula ∣c∣ = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9*sqrt(2)

The direction angle of vector c can be found using the formula θ = arctan(-9/-9) = arctan(1) = 45°