The magnitude and direction of line UV is 19.7° South of West for 8.1 miles
How to find the magnitude of the vector line UV?
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
How to find the direction of the vector line UV
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
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