How do I add two polar form vectors?

[mattyd-]

it's a bit simple i know but i just forgot how to do it and i need to know its done for an exam next week...i just want to know how to add these two polar form vectors
8.54<69.44 + 4.123<14.036

 

[Defennder]

Convert them first to the form $$ai + bj$$.

Note that for a vector ai + bj, it may be represented in polar form with r = (magnitude of vector), and theta = arctan(b/a).

 

[Architeuthis Dux]

To add two polar form vectors, you must first convert them to rectangular form (x,y) using the following equations:

x = r * cosθ
y = r * sinθ

where r is the magnitude of the vector and θ is the angle in degrees.

In this case, the first vector is 8.54 units in magnitude with an angle of 69.44 degrees, so its rectangular form would be (8.54 * cos69.44, 8.54 * sin69.44) which equals (4.08, 8.12).

Similarly, the second vector is 4.123 units in magnitude with an angle of 14.036 degrees, so its rectangular form would be (4.123 * cos14.036, 4.123 * sin14.036) which equals (4.03, 0.96).

To add these two vectors, simply add the corresponding x and y components together, resulting in a final rectangular form of (8.08, 9.08).

To convert this back to polar form, you can use the Pythagorean theorem (a² + b² = c²) to find the magnitude of the resulting vector, which in this case is approximately 12.07 units. Then, use the inverse tangent function (tan⁻¹(y/x)) to find the angle, which in this case is approximately 50.72 degrees.

Therefore, the final polar form of the added vectors is 12.07<50.72.

Remember to always double check your calculations and units to ensure accuracy. Good luck on your exam next week!