Ap physics Unit 1: adding and subtracting vectors formula

Resultant= the sum of adding two vectors or the hypotenuse of a vector with x and y components.

r²=X²+y²- use this formula to find the side lengths when adding vectors

r= \sqrt{X^2 + y^2}, where r represents the resultant vector magnitude.

tan θ= y/x

θ = tan^-1(y/x)- formula for magnitude and direction of angle that the vector makes with the x axis

Law of cosines: C²=a²+b²-2ab*cos c- this formula can be used for adding or subtracting vectors that are non right triangles

Law of sines: ( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} ) - this formula can also assist in solving for unknown sides or angles when dealing with non-right triangles.

When adding two vectors with x and y components, add the x components together and the y components together and then us c=\sqrt{x²+y²} to find the magnitude of the resultant vector.

|Resultant| cos θ= x component

|Resultants| sin θ- y component

Adding vectors- A+B=C(same as resultant)

Subtracting- A+(-b)=C(same as resultant)