Vector A is 2cm long and 60degree Above the x axis in first quadrant . Vector B is 2cm long and 60degree below the x axis in the fourth quadrant .the sum of vector A and B is a vector of magnitude.
To find the sum of vector A and vector B, we can add their components.
Let's start by finding the components of vector A and vector B.
For vector A:
- Length: 2 cm
- Angle: 60 degrees above the x-axis in the first quadrant
To find the x-component of vector A, we can use the formula:
x-component = length * cos(angle)
So, for vector A:
x-component of A = 2 cm * cos(60 degrees)
To find the y-component of vector A, we can use the formula:
y-component = length * sin(angle)
So, for vector A:
y-component of A = 2 cm * sin(60 degrees)
Now, let's find the components of vector B:
For vector B:
- Length: 2 cm
- Angle: 60 degrees below the x-axis in the fourth quadrant
To find the x-component of vector B, we can use the formula:
x-component = length * cos(angle)
So, for vector B:
x-component of B = 2 cm * cos(60 degrees)
To find the y-component of vector B, we can use the formula:
y-component = length * sin(angle)
So, for vector B:
y-component of B = 2 cm * sin(60 degrees)
Now that we have the components of vector A and vector B, we can add them to find the sum of vector A and vector B.
Sum of x-components = x-component of A + x-component of B
Sum of y-components = y-component of A + y-component of B
Once we have the sum of x-components and the sum of y-components, we can use the Pythagorean theorem to find the magnitude of the sum vector.
Magnitude of the sum vector = sqrt((Sum of x-components)^2 + (Sum of y-components)^2)
Vhj
draw a diagram. using the law of cosines, the length of the sum is
x^2 = 2^2 + 2^2 - 2*2*2*cos60°
All angles are measured CCW from +x-axis.
A + B = 2cm[60o] + 2cm[300o].
X = 2*Cos60 + 2*Cos300 = 1 + 1 = 2 cm.
Y = 2*sin60 + 2*sin300 = 1.73 - 1.73 = 0.
A+B = 2 + 0i = 2cm[0o].