A[b] VECTOR[/b] is a mathematical quantity with both magnitude and direction, represented with a directed line segment, or an arrow.[br][list][*]A [b]standard position vector[/b] has its initial point at the origin and its terminal point at (a, b).[br][/*][*]The [b]components[/b] of a standard position vector are given as [math]\left\langle a,b\right\rangle[/math].[/*][*]The[b] magnitude (length)[/b] of vector [math]\vec{u}[/math] is denoted as [math]|\vec{u|}[/math]. [br][/*][*]The [b]direction angle [/b]is the angle the vector makes with the positive x-axis.[/*][/list][br]For a standard position vector, the components, direction angle, and magnitude can be calculated using right-triangle trigonometry:[br]Components: [math]<|\vec{u}|cos\theta,|\vec{u}|sin\theta>[/math] Direction: [math]tan\theta=\frac{b}{a}[/math] Magnitude: [math]\mid\vec{u|}=\sqrt{a^2+b^2}[/math][code][br][/code][br][i][color=#cc0000]Interactive Graph: Move the yellow dot to adjust the vector. Reason out the components of the vector and verify you can calculate the components, the direction angle, and the magnitude of a standard position vector.[/color][/i]