Lesson 6 complex roots of a polynomial equation
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The document discusses complex roots of polynomial equations. It notes that any polynomial with complex roots will have roots that come in conjugate pairs. It asks questions about the relationship between the coefficients of a polynomial and the sum and product of its roots. Specifically, it asks the reader to find the values of a and b for a quartic polynomial given that two of its roots are 3i and 1-2i.
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S7 investigating vectors student worksheet (colour)
This document contains a student worksheet for investigating vectors in 2D and 3D using Autograph software. It includes tasks on expressing vectors in terms of other vectors, finding vector equations of lines given conditions, calculating lengths and angles of vectors, and using vectors to solve geometric problems in 2D and 3D. The worksheet guides students through using Autograph's vector tools to explore and check their work.
More scalar product
The document discusses scalar products of vectors and different types of vector relationships. It asks to define the scalar product using notation, calculate products of perpendicular and parallel vectors, and explain the difference between parallel and coincident vectors with a diagram. Perpendicular vectors have a scalar product of 0, parallel vectors maintain the same direction but their scalar product depends on length and angle, and coincident vectors overlap completely and have the greatest possible scalar product.
Converting vector equation of a line to cartesian form
The document describes how to convert a vector equation of a line to Cartesian form. A vector equation defines a line using a point (a,b,c) on the line and a direction vector (k,m,n). It explains how to write the x, y, z coordinates in terms of λ and rearrange to make λ the subject, then equate the expressions to find the Cartesian equation of the line. The Cartesian equation defines the line using the standard x, y, z variables.
The scalar product form for the equation of a plane
The document discusses deriving the scalar product form of the equation of a plane. It defines two points A and P on the plane and their position vectors a and r. It explains that the vector from A to P, AP, is equal to r - a. Using the scalar product of the position vector r and the normal vector n to the plane, along with the position vector a, allows obtaining the scalar product equation of the plane, r·n = a·n. This equation can then be written in Cartesian form.
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Your rubric multimedia project how tall is the sports block_
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