Explanation:
Vector A:
Magnitude: 8
Angle: 132 degrees
To find the x and y components of vector A:
x-component (A_x) = 8 * cos(132°)
y-component (A_y) = 8 * sin(132°)
Vector B:
Magnitude: 5
Angle: 260 degrees
To find the x and y components of vector B:
x-component (B_x) = 5 * cos(260°)
y-component (B_y) = 5 * sin(260°)
Now, calculate the x and y components:
For vector A:
A_x = 8 * cos(132°) ≈ -3.464
A_y = 8 * sin(132°) ≈ 6.928
For vector B:
B_x = 5 * cos(260°) ≈ -4.082
B_y = 5 * sin(260°) ≈ -2.588
Next, add the x and y components of both vectors together to get the resultant vector:
Resultant x-component (R_x) = A_x + B_x ≈ -3.464 - 4.082 ≈ -7.546
Resultant y-component (R_y) = A_y + B_y ≈ 6.928 - 2.588 ≈ 4.34
Now, you have the x and y components of the resultant vector. To find its magnitude (R) and angle (θ), you can use the Pythagorean theorem and trigonometric functions:
R = √(R_x^2 + R_y^2) ≈ √((-7.546)^2 + (4.34)^2) ≈ √(56.952 + 18.8356) ≈ √75.7876 ≈ 8.704
θ = arctan(R_y / R_x) ≈ arctan(4.34 / -7.546) ≈ arctan(-0.575) ≈ -29.76 degrees (approximately)
So, the resultant vector has a magnitude of approximately 8.704 and an angle of approximately -29.76 degrees. Note that the negative angle means it's measured clockwise from the positive x-axis.