Consider the vectors A = 2.00 i + 7.00 j and B = 3.00 i - 2.00 j.
(a) Sketch the vector sum C = A + B and the vector subtraction D = A - B.
(b) Find analytical solutions for C and D first in terms of unit vectors and then in terms of polar coordinates, with angles measured with respect to the positive x axis.
I just can't figure out what the degree should be for the D vector polar coordinate
D=-i+9j
angle of D= arctan 9
A+B = (2+3)i + (7-2)j = 5i+5j
A-B = -i+9j
just draw a triangle with hypotenuse from (0,0) to (-1,9)
tanθ = 9/-1
θ = 180+83.66° = 263.66° or -96.34°
Oops. That would be
180-83.66 = 96.34°
thank you! the answer was 96.3
To find the polar coordinates for vector D (A - B), you need to calculate the magnitude and angle of the vector.
Let's start by finding the magnitude of vector D using the formula:
|D| = sqrt((Dx)^2 + (Dy)^2)
Dx represents the x-component of vector D, and Dy represents the y-component of vector D.
In this case, Dx = Ax - Bx = 2.00 - 3.00 = -1.00 and Dy = Ay - By = 7.00 - (-2.00) = 9.00.
Now, substitute these values into the magnitude formula:
|D| = sqrt((-1.00)^2 + (9.00)^2) = sqrt(1.00 + 81.00) = sqrt(82.00) = 9.06
The magnitude of vector D is approximately 9.06.
Next, let's find the angle of vector D (θ) with respect to the positive x-axis. We can use trigonometry to calculate this angle.
Using the formula:
θ = arctan(Dy / Dx)
Substitute the values of Dx and Dy into the formula:
θ = arctan(9.00 / -1.00) ≈ -81.87 degrees
The angle θ of vector D is approximately -81.87 degrees. Note that the negative sign indicates a counterclockwise rotation from the positive x-axis.
Therefore, the polar coordinates for vector D (A - B) are approximately (9.06, -81.87 degrees).