Scalars, vectors and moments GapFill

All quantities can be described as either scalars or vectors. Scalars are quantities with  magnitude and directionmagnitude and sizemagnitude but no directionno units, while vectors are quantities with  magnitude and directionunitsmagnitude but no directionmagnitude and size.
Vectors can be resolved in components. To find the size of the vertical component of a vector, the equation  v × cos(θ)v × sin(θ)θ × sin(v)θ × cos(v) can be used, and to find the horizontal component, the equation  v × cos(θ)v × sin(θ)θ × sin(v)θ × cos(v) can be used, where θ is the angle between the horizontal and the vector and v is the size of the vector.
To find the size and angle of a vector from its components, use  v(x) ÷ v(y)√(v(x) + v(y))√(v(x)² + v(y)²)v(x) × v(y) to find its size, and  √(v(x)² + v(y)²)tan(θ) = v(y) ÷ v(x)tan(θ) = v(y) × v(x)θ = cos(v(y)) + sin(v(x)) to find its angle.
A moment is a force acting to rotate an object around a point. The moment of a force is given by the equation  √(force² + (perpendicular distance)²)force ÷ (perpendicular distance)force × (perpendicular distance)1/2 × force × (perpendicular distance)².