Three vectors, A, B, C have the following x and y components: Ax = 6.7, Ay= -2.3; Bx = -5.5, By = 4.5; Cx = 3.2, Cy = 7.2.
What is the magnitude of A + B + C ?
add the x components; add the y components.
then magnitude= sqrt(sumx^2+sumy^2)
X = hor = 6.7 + (-5.5) + 3.2 = 4.4.
Y = ver = -2.3 + 4.5 + +7.2 = 9.4.
R^2 = X^2 + Y^2,
R^2 = (4.4)^2 + (9.4)^2,
R^2 = 19.36 + 88.36,
R^2 = 107.72,
R = 1O.4 = Resultant = Magnitude.
To find the magnitude of vector A + B + C, we need to calculate the sum of the x and y components of the three vectors and then find the magnitude of the resulting vector.
First, let's calculate the sum of the x components (Ax, Bx, Cx):
Ax + Bx + Cx = 6.7 + (-5.5) + 3.2 = 4.4
Next, let's calculate the sum of the y components (Ay, By, Cy):
Ay + By + Cy = -2.3 + 4.5 + 7.2 = 9.4
Now we have the x and y components of the resulting vector. To find the magnitude, we can use the Pythagorean theorem:
Magnitude = √(x^2 + y^2)
Magnitude = √(4.4^2 + 9.4^2)
Magnitude = √(19.36 + 88.36)
Magnitude = √107.72
Magnitude ≈ 10.38
Therefore, the magnitude of A + B + C is approximately 10.38.
To find the magnitude of A + B + C, we first need to find the sum of these three vectors and then calculate the magnitude of the resulting vector.
To find the sum of the vectors A, B, and C, we add their corresponding components:
Ax + Bx + Cx = 6.7 + (-5.5) + 3.2 = 4.4
Ay + By + Cy = (-2.3) + 4.5 + 7.2 = 9.4
Therefore, the sum of the vectors A, B, and C is a new vector with x-component 4.4 and y-component 9.4.
To calculate the magnitude of this resulting vector, we can use the Pythagorean theorem:
Magnitude = sqrt((x^2) + (y^2))
Magnitude = sqrt((4.4^2) + (9.4^2))
Magnitude = sqrt(19.36 + 88.36)
Magnitude = sqrt(107.72)
Magnitude ≈ 10.38
Therefore, the magnitude of the vector A + B + C is approximately 10.38.