2AB B terminal point A initial point Quantities that we measure that have magnitude but not direction are called scalars.Quantities such as force, displacement or velocity that have direction as well as magnitude are represented by directed line segments.BterminalpointABorThe length isAinitialpointor
3B terminal point A initial point A vector is represented by a directed line segment.Vectors are equal if they have the same length and direction (same slope).
4yA vector is in standard position (0) if the initial point is at the origin.xThe component form of this vector is:
5yA vector is in standard position if the initial point is at the origin.xThe component form of this vector is:The magnitude (length) ofis:
6If P(p1, p2) and Q(q1, q2) are the initial and terminal points of a directed line segment, the component form of the vector v represented byisThis means the length (magnitude) of v is
7A vector has an initial point at (-3, 4) and terminal point at (-5, 2). (-3,4)PThe component form of(-5,2)Qis:v(-2,-2)
8If v is a nonzero vector in plane, then the vector has length 1 and the same direction as v.u is called a unit vector in the direction of v.is the zero vector and has no direction.
9Find a unit vector in the direction of Ex.Find a unit vector in the direction ofOne of the vector operations says I can multiply a scalar by both components of a vector.We can make sure this is a unit vector by seeing if the magnitude = 1.