Respuesta :
According to estimates, FG has a magnitude of 2√5.
The vector direction of FG is given as = 63.43°. (angle formed in the 1st quadrant with anti-clockwise direction).
What exactly would a distance formula imply?
The distance formula is used in complex numbers to show the plane in addition to its magnitude. Distance formulas can also be used to determine the actual the distances between two planes in three- and n-dimensional planes.
Now, in answer to the question posed;
F and G have coordinates of (-1,10) and (1,-12), respectively.
The formula for calculating the distance between points A and B is as follows:
FG² = (x₂ - x₁)² + (y₂ - y₁)²
FG = √[(x₂ - x₁)² + (y₂ - y₁)²]
The coordinates for the points F and G's are-
(x₁,y₁) = (-4,0) and (x₂,y₂) = (-6,-4).
Substituting the given values in the distance formula;
FG = √[(-6 + 4)² + (-4 + 0)²]
FG = √[(-2)² + (-4)²]
FG = √[4 + 16] = √20
FG = 2√5 (magnitude of the vector FG)
Estimate the direction of this same vector FG now. The angle formed by a vector with a horizontal line defines its direction.
Use one of the following formulas to calculate the direction of a vector.
tan Ф = Δy/Δx
Where, x = horizontal change
and, y = vertical change
tan Ф = (y₂ - y₁)/(x₂ - x₁)
= (-4 + 0)/(-6 + 4)
tan Ф = -4/(-2) = 2
Ф = 63.43° (angle lies with in the first quadrant with anticlockwise direction).
As a result, the distance between F and G is determined to be 2√5. (the same as the magnitude of a given vector FG).
More details about the distance formula can be found here.
brainly.com/question/24386522
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