Vectors

MEX-V1 Further Work with Vectors

• understand and use a variety of notations and representations for vectors in three dimensions

  not written yet

  • define the standard unit vectors, and

    not written yet

  • express and use a vector in three dimensions in a variety of forms, including component form, ordered triples and column vector notation

    not written yet

• perform addition and subtraction of three-dimensional vectors and multiplication of three-dimensional vectors by a scalar algebraically and geometrically, and interpret these operations in geometric terms

  not written yet · needs a worked example

• define, calculate and use the magnitude of a vector in three dimensions

  not written yet · needs a worked example

  • establish that the magnitude of a vector in three dimensions can be found using:

    not written yet · needs a worked example

  • convert a non-zero vector into a unit vector by dividing by its length:

    not written yet · needs a worked example

• define and use the scalar (dot) product of two vectors in three dimensions AAM

  not written yet

  • define and apply the scalar product to vectors expressed in component form, where , and

    not written yet · needs a worked example

  • extend the formula for three dimensions and use it to solve problems

    not written yet · needs a worked example

• prove geometric results in the plane and construct proofs in three dimensions (ACMSM102)ACMSM102

  not written yet · needs a worked example

• use Cartesian coordinates in two and three-dimensional space

  not written yet

• recognise and find the equations of spheres

  not written yet · needs a worked example

• use vector equations of curves in two or three dimensions involving a parameter, and determine a corresponding Cartesian equation in the two-dimensional case, where possible (ACMSM104) AAMACMSM104

  not written yet · needs a worked example

• understand and use the vector equation of a straight line through points $A$ and $B$ where $R$ is a point on $AB$, , , $\lambda$ is a parameter and

  not written yet

• make connections in two dimensions between the equation and $y=mx+c$

  not written yet

• determine a vector equation of a straight line or straight-line segment, given the position of two points or equivalent information, in two and three dimensions (ACMSM105)ACMSM105

  not written yet · needs a worked example

• determine when two lines in vector form are parallel

  not written yet · needs a worked example

• determine when intersecting lines are perpendicular in a plane or three dimensions

  not written yet · needs a worked example

• determine when a given point lies on a given line in vector form

  not written yet · needs a worked example