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
- (x₁, y₁) = (2, 3) and
- (x₂, y₂) = (-2, -4)
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
- (x₁, y₁) = (2, 3) and
- (x₂, y₂) = (-2, -4)
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
Learn more about vectors here:
brainly.com/question/26700114
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