# Vectors

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• Created by: eleanor
• Created on: 22-04-15 17:55
• Vectors
• Cartesian Vectors
• i= movement in x direction
• j in y direction
• k in z direction
• magnitude of the vector = lentgh of it
• =
• direction of vectors in 2D
• sketch the vector
• we want the angle that the vector makes with the x axis  use socahtoa
• distance between two points is the difference between each coordinate square then sqaurerooted
• Parallel Vectors
• parallel vectors have the same direction and are multiplies of each other
• so 2i + 3j + 4k is parallel to 6i + 9j + 12k
• Unit Vectors
• these have a magnitude of 1
• find the unit vector parallel
• step one find the magnitude
• step 2: divide by the magnitude to get the unit vector
• Scalar Product : Dot product           a  b = x1x2 + y1y2 + z1z2
• Straight Lines
• r = p + Kq
• position vector of a point on the line
• a scalar (number)
• Direction vector
• method 1- given 2 points that lie on the line
• find the vector equation of the line joining 2 vectors
• 1. find the direction vector AB = b-a
• 2. r = point A + K(direction vector)
• method 2- given a point on the line and a parallel vector
• if it passes through point A use that  as the point  and then use the direction vector that the line is parallel to
• Method 3-
• Given a point on the line and told that it is parallel to an axis
• use point A that you are given that make the direction vector by putting a 1 in the coordinate of the axis
• Perpendicular Lines: if a dot b = 0
• a and b must be direction vectors for this to work
• convert the lines into column vectors
• find the scalar product using the direction vectors
• Parallel lines: if a dot b = |a| dot |b|
• angles between 2 straight lines
• cos(x) = a.b/|a||b|
• identify the direction vectors then find the magnitudes
• find the scalar product  then sub into formula
• finding if 2 line intersect
• step 1: set the two equations of the line equal to each other then evaluate components separately
• solve 2 of the equations simultaneously to find s and t then substitute them into the third equation and if they are equal they intersect
• finding if a point lies on a line
• equate the position vector of the point to the equation of the line
• equate the i, j, k components separately to get 3 equations
• solve each equation to find the unknown if they are all the same the cooridnate does lie o the line
• finding the shortest distance from a point
• find any lengths and angles needed in the triangle
• then use socahtoa to find the missing side