Show:
Equations of a Line in R2
Scalar Equation of a Line in R2
Vector, Parametric, and Symmetric Equations of a Line in R3
Vector and Parametric Equations of a Plane
The Scalar Equation of a Plane
100
What is the vector and parametric equation of a line passing through point A(1,4) with direction vector (-3,3)?
Vector equation: r=(1,4)+t(-3,3), tER Parametric equations: x=1-3t, y=4+3t, tER
100

What is the Scalar Equation pf the line passing through A(9,8), which has n=(5,3) as its normal?

5x+3y-69=0

100
What are the symmertric equations for U(-2,4,-1) and H(-2,3,5) ?
(y-3) /-1 = (z-5) /6 , x+2
100
What are the coordinates of a point that is on the plane x=2m, y=-8m+3n, z=-1-6m-7n, m,nER ?
(0,0,-1)
100

What is the Scalar Equation of a plane, where point A(1,2,2) is a point on the plane with normal (-1,2,6) ?

x-2y-6z+15=0

200
What is the point at which the line L:r=(1,2)+t(-1,4), tER intersects the x-axis.
A(1.5,0)
200

What is the Scalar equation of the line: r=(1,2)+t(-1,1) ?

x+y-3=0

200
plane: r= (6,-2,3)+s(1,3,0)+t(2,2,-1) , s,tER What is the point of intersection between the plane and the z-axis ?
POI (0,0,8) (linear systems)
200

What are the 4 ways that a plane can be determined?

1) a line and a point not on the line 2) three non-collinear points 3) two intersecting lines 4) two parallel and non-coincident lines

200

What is the Scalar form of the plane whose equation in vector form is r=(1,2,-1)+s(1,0,2)+t(-1,3,4)

Scalar equation: 2x+2y-z-7=0

300
What is the vector equation of the line y=3/4x+2 ?
r=(0,2)+t(4,3), tER
300
What is the acute angle between x-3y+6=0 and x+2y-7=0 ?
Acute angle= 45 degrees
300
What is the symmetric equation of the line passing through D(7,1,-2) and E(10,-3,8) ?
(x-7) /3 = (y-1) /-4 = (z+2) /10
300
Does the equation r=(-1,0,-1)+s(2,3,-4)+t(4,6,-8) represent the equation of a plane? Explain.
No, it does not represent the equation of a plane because the direction vectors are scalar multiples of each other.
300
Why can't a symmetric equation exist for a plane?
There are two parameters.
400
The parametric equations of a line are given as x=-14-2s, y=8+s, sER. This line crosses the x-axis at the point with the coordinates A(d,0) and crosses the y-axis at the point with coordinates B(0,e). If O represents the origin, what is the area of the triangle ABO?
Area (AOB)= 1 unit squared
400

What is the Scalar equation for a line that has parametric equations x=3-t , y=-2-4t, tER ?

4x-y-14=0

400
What are the symmetric equations for the line passing through the points D (-1,0,0) and E (-1,1,0)
Not possible since 2 coordinates of the direction vector are zero.
400
Do the following equations represent the same plane: r=s(-3,2,4)+v(-4,7,1) , s, vER and r= u(-1,5,-3)+t(-1,-5,7) ,u,tER
No, the equations do not represent the same plane. (Linear combination)
400
What is the vector equation of the plane that is parallel to the yz-plane, and has a point G(2,7,9).
r=(2,7,9)+ s(0,1,0)+t(0,0,1) , s,tER