an airplane flies in the path shown by the vector line UV on the graph below. what is the magnitude and direction of line UV? (1

Question

2 years ago

15

unit represents 1 mile)

1 answer:

GaryK [48] · Answer 1 · 2023-05-23T14:40:59+03:00

The magnitude and direction of line UV is 19.7° South of West for 8.1 miles

<h3>How to find the magnitude of the vector line UV?</h3>

The magnitude of the vector line UV is given by the length of the line UV,

d = √[(x₂ - x₁)² + (y₂ - y₁)²] where

Substituting the values of the variables intot he equation, we have

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(-2 - 2)² + (-4 - 3)²]

d = √[(-4)² + (-7)²]

d = √[4² + 7²]

d = √[16 + 49]

d = √65

d = 8.06 miles

d ≅ 8.1 miles

So, the magnitude of vector line UV is 8.1 miles

<h3>How to find the direction of the vector line UV</h3>

The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where

Substituting the values of the variables into the equation, we have

Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]

Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]

Ф = tan⁻¹[(-7)/(-4)]

Ф = tan⁻¹[7/4]

Ф = tan⁻¹[1.75]

Ф = 60.26°

Ф ≅ 60.3°

Its bearing from the north-south line is α = 90° - Ф

= 90° - 60.3°

= 19.7°

So, its direction is 19.7° South of West

So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles

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