Vectors A vector is a quantity that has both magnitude and direction. We are familiar with our 2-Dimensional Cartesian Plane but let us take a look at our 3 dimensional Cartesian Plane. In our 3 dimensional plane we have 3 axes, the x-axis, y-axis and z-axis. As such when we state a vector in this plane we must state it using a 3 co-ordinate system. In the above diagram we have the vector Since our plane is defined in the form then the vector has the co-ordinates . Unit Vectors A unit vector is a vector that has a magnitude of 1 unit and acts in the direction of the vector. We can define the unit vectors such that, represents a unit vector in the direction of the x-axis, as a unit vector in the y-axis and as a unit vector in the z-axis. As such, a vector , can be written in multiple forms. We can define in polar form as or vector form as Operations on Vectors Addition When we add 2 vectors we add the corresponding coefficients of the unit vectors given the vectors then Subtraction When we subtract 2 vectors we subtract the corresponding coefficients of the unit vectors given the vectors then Multiplication by a Scalar When we do scalar multiplication we multiply the coefficients of the unit vectors by the scalar. given the vector and the scalar quantity , then Equality Two vectors are said to be equal if the values of the corresponding unit vectors are equal. given the vectors then Types of Vectors Position Vector A position vector is a vector that has a fixed location on our Cartesian Plane. In general position vectors have a fixed position in relation to the Origin. Therefore given the point , we can define the position vector Unit Vector A unit vector is a vector that has a magnitude of 1 unit and acts in the direction of the original vector. Since parallel vectors move/act in the same direction, we can use this knowledge to derive unit vectors. In general 2 vectors are said to be parallel if we can represent one vector as a multiple of the other. i.e. given the vectors then (where is a scalar) Simply put Displacement Vector A displacement vector is a vector whose position is not fixed in space. In general displacement vectors are vectors that lie between two or more given points. The position vectors of the points are used to determine the displacement vector. Magnitude of a Vector Let . The magnitude(length) or modulus of Scalar or Dot Product Let The Dot or Scalar product of is given by Angle between two Vectors Let If the angle between is then Or June 2016 June 2014