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

Formula used to find the resultant vector magnitude when adding vectors that make right angles

Magnitude of the resultant vector (r)

r = √(X² + y²), where r represents the resultant vector magnitude.

tan θ = y/x

Formula used to find the angle θ that the vector makes with the x-axis.

Law of cosines

C² = a² + b² - 2ab cos(c), used for adding or subtracting non-right triangle vectors.

Law of sines

(a/sin A) = (b/sin B) = (c/sin C), assists in solving for unknown sides or angles in non-right triangles.

Adding vectors

Add the x components together and the y components together to find the resultant.

|Resultant| cos θ

Equals the x component of the vector.

|Resultant| sin θ

Equals the y component of the vector.

Subtracting vectors

A + (-B) = C (the resultant).

Adding vectors notation

A + B = C (same as resultant).

tan^-1(y/x)- formula for direction and magnitude of angle the vectors make with the x axis.