Vector and Parametric Equations of Lines in 2D
True or False: Plugging in any real number for “t” will allow you to obtain the coordinates of other points on the line.
True
What does it mean to be coincident?
To be parallel and to have a shared point
True or False: Two lines that are parallel and share a common point do not represent the same line
False
True or False: You need one direction vector to get the equation of a plane
False
Why was 6 afraid of 7
Identify the direction vector and a point on the following lines r = (3, 4) + t (2,1), tER
Direction Vector: (2, 1), Point: (3, 4)
What is the normal axis of a line
The normal axis is a perpendicular line and is drawn from the origin
What makes up the vector equation of a line in 3D
The direction vector, the parameter, and a general point on the line
When is the cross product used when finding the equations of a plane
The normal of a plane is the cross product of any two direction vectors defined on the plane
Why was math class so long?
The teacher kept going off on a tangent.
Transform the parametric equation x = 1 - 3t and y = 4 + 3t into a vector equation
r = (1, 4) + t (-3,3), tER
What can A and B represent in an cartesian equation (Ax+By+C=0)
The normal axis
What are the restrictions of the symmetric equation of a line
The components of the direction vector cannot equal zero
What are the 4 ways to define a plane.
1. A line and a point not on the line, 2. Three non-collinear points, 3. Two intersecting lines, 4. two non-coincident and parallel lines
Whats long and hard and scary when you first see it?
Calculus Homework!
For the points A(½ , -3) and B (¾ , ½ ), would the direction vector be equal for AB and BA.
No, the magnitude is the same but the direction is not. AB = (¼ ,7/2) BA = (-¼ , -7/2)
If a point passes through (0,1) and (0,2), what could be the direction vector for this line
(0,1)
Write the following vector equation : r = (3,7,1) + t(1,-2,4) as a parametric equation
x = 3 + t; y = 7 - 2t; z = 1 + 4t
Determine a vector equation for the plane containing the points P(-2, 3, 3), Q(-3, 4, 8) and R(1, 1, 10).
r = (-2, 2, 3) + s(-1, 2, 5) + t(3, -1, 7); t & s are all real numbers
What did the 3D Vector say after making a bad joke?
i j k
A line is defined by the parametric equations x = -2 - t and y = 4 +2t. Prove if the point (-9, 18) lies on this line?
(-9,18) is a point on the line, when t = 7
For what value of k makes 3x-4y+4=0 and 6x-8y+k=0 coincidental
8
Does the point A(5,-1,3) exist on the line passing through the points B(-1,2,1) and C(-4,3,0)
The point does not exist on the plane.
Determine the Cartesian equation of the plane that passes through the points (1, 4, 5) and (3, 2, 1) and is perpendicular to the plane 2x - y + z - 1 = 0.
3x + 5y - z - 18 = 0
Why can’t a person go into the woods if they fail calculus?
There are too many natural logs for their liking