
Parametric Equations of Line Intersections

Interactive Video
•
Mathematics, Science
•
9th - 12th Grade
•
Hard

Mia Campbell
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the parametric equations for the line of intersection between two planes?
Calculate the area of the planes
Identify the angle between the planes
Determine a direction vector and a point on the line
Find the midpoint of the planes
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can the direction vector for the line of intersection be found?
By dividing the normal vectors of the planes
By finding the cross product of the normal vectors of the planes
By adding the normal vectors of the planes
By subtracting the normal vectors of the planes
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the cross product of the normal vectors in this context?
It calculates the area of the intersection
It determines the angle between the planes
It provides a direction vector for the line of intersection
It gives the midpoint of the line
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When finding a point on the line of intersection, why is the x-coordinate set to zero?
To simplify the calculations
To match the parametric equation format
Because the x-coordinate is always zero
To eliminate the z-coordinate
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What method is used to solve the system of equations to find the y and z components of the intersection point?
Substitution
Graphical method
Elimination
Matrix inversion
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the parametric equations for the line of intersection using the given direction vector?
x(t) = 0 + 3t, y(t) = 1 + t, z(t) = -2 + 7t
x(t) = 0 - 3t, y(t) = 1 - t, z(t) = -2 - 7t
x(t) = 0 - 63t, y(t) = 1 - 21t, z(t) = -2 - 147t
x(t) = 0 + 63t, y(t) = 1 + 21t, z(t) = -2 + 147t
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why might it be simpler to use a different scalar multiple for the direction vector?
To change the direction of the line
To simplify the coefficients in the parametric equations
To eliminate the need for a point on the line
To make the equations more complex
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