Vectors
- Created by: eleanor
- Created on: 22-04-15 17:55
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- Vectors
- Cartesian Vectors
- i= movement in x direction
- j in y direction
- k in z direction
- j in y 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
- sketch the vector
- 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
- parallel vectors have the same direction and are multiplies of each other
- 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
- i= movement in x direction
- 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)
- find the vector equation of the line joining 2 vectors
- 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
- r = p + Kq
- 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
- step 1: set the two equations of the line equal to each other then evaluate components separately
- 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
- equate the i, j, k components separately to get 3 equations
- equate the position vector of the point to the equation of 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
- find any lengths and angles needed in the triangle
- Cartesian Vectors
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