Three vectors are specified as A is 5 m at 45o north of east, B is 7 m at 60o east of south, and C is 4 m at 30o west to south.?Find the magnitude and direction of their sum.

A = (3.5,3.5)

B = (6.1,-3.5)
C = (-2.0,-3.5)

Now just add up the (x,y) components and convert back to magnitude and direction form.

To find the magnitude and direction of the sum of three vectors A, B, and C, we need to add the vectors together algebraically.

Let's break down each vector into its x-component and y-component using trigonometry.

Vector A:
- Magnitude: 5 m
- Direction: 45° north of east

To find the x-component of vector A, we need to find the component in the east direction. We can do this by using the cosine function:
A_x = A * cos(45°)

Substituting the values, we get:
A_x = 5 m * cos(45°)

Calculating this, we find:
A_x ≈ 3.535 m

To find the y-component of vector A, we need to find the component in the north direction. We can do this by using the sine function:
A_y = A * sin(45°)

Substituting the values, we get:
A_y = 5 m * sin(45°)

Calculating this, we find:
A_y ≈ 3.535 m

Thus, vector A can be written as:
A = (3.535 m, 3.535 m)

Similarly, we can find the x- and y-components of vectors B and C:

Vector B:
- Magnitude: 7 m
- Direction: 60° east of south

B_x = B * cos(-60°)
B_y = B * sin(-60°)

Vector C:
- Magnitude: 4 m
- Direction: 30° west to south

C_x = C * cos(30°)
C_y = C * sin(30°)

Now we can add the x- and y-components of the three vectors together:

Sum_x = A_x + B_x + C_x
Sum_y = A_y + B_y + C_y

Substituting the known values, we have:

Sum_x = 3.535 m + (7 m * cos(-60°)) + (4 m * cos(30°))
Sum_y = 3.535 m + (7 m * sin(-60°)) + (4 m * sin(30°))

Calculating these values will give you the components of the sum vector.

Finally, we can use these components to find the magnitude and direction of the sum vector using the Pythagorean theorem and trigonometry.

Magnitude of the sum vector:
Magnitude = sqrt(Sum_x² + Sum_y²)

Direction of the sum vector:
Direction = arctan(Sum_y / Sum_x)

Calculating these values will give you the magnitude and direction of the sum vector formed by vectors A, B, and C.