9.2 Vectors in the Plane

Vectors in the Plane

[*] - come back to these questions after reading section 9.5

Let P=(1,3) and Q=(2,1) be points in (ℝ^2).

Graph these points.

Graph the vector (OverVector[PQ]).  What are its components?

Graph the equivalent vector with base at the origin.

Graph an equivalent vector that does not have its base at the origin.

Graph a parallel vector that is not equivalent.

Determine the length of the vector (OverVector[PQ]).  Explain why this is the length.

Draw the line that passes through the points P and Q.

[*] Find a standard equation, in the form a x+b y=c, describing the line.

[*] Find a parametric equation, in the form {(x,y)=(a,b)+t (c,d):-∞<t<∞} , describing the line.

[*] Find a symbolic representation of the line segment between the points P and Q.

Consider the graphed vectors.

Find the components of the vectors u= (OverVector[OP]) and v=(OverVector[OQ]).   

u=<_____, _____>

v=<_____, _____>

Determine 3u and u+v numerically and graphically.

Write w=⟨2,8⟩ as a linear combination of u and v.