Parametric Dialectic
The Plane Truth
You're So Far Away
What's Your Angle?
Miscellaneous
100
The location of the point following the line determined by the parametric equations x(t) = 3t + 5 y(t) = -2t + 1 at time t = 4.
What is (17, -7)?
100
The equation of the plane through the point (3, -4, 5) and parallel to the yz-plane.
What is x = 3?
100
The distance between the point ( 2, 3, -4) and the plane given by x - y + 2z = 4.
What is 13/Sqrt(6)?
100
The angle of intersection between the planes given by 3x + 4y - z + 12 = 0 and x - y - z - 5 = 0
What is 90 degrees?
100
The graph of the vector-valued function given by r(t) = (1 - t)i + (3t)j + (2t)k looks like this
What is a line through the point (1, 0, 0) and parallel to the vector <-1, 3, 2>?
200
The set of parametric equations of the line passing through the point (5, 0, -3) and parallel to v = <6, -2, 1>
What is x = 5 + 6t, y = -2t, and z = -3 + t?
200
The point-normal form of the equation through the point (0, 3, 5) and perpendicular to the vector <-2, 1, 6>
What is -2(x) + (y - 3) + 6(z - 5) = 0
200
The distance between the point (-3, 0, 9) and the plane given by 5x - y + 2z - 3 = 0.
What is 0?
200
The angle of intersection between the planes given by 3x + 2y - z + 12 = 0 and x - y - z - 5 = 0
What is 72 degrees?
200
The domain of the vector-valued function given by r(t) = (t^3)i - (Sqrt(1 + t))j - k
What is t >= -1?
300
The set of parametric equations of the line passing through the points (4, 2, -1) and (0, -3, 8).
What is x = 4 - 4t, y = 2 - 5t, z = -1 + 9t OR x = 4 + 4t, y = 2 + 5t, z = -1 - 9t OR x = 0 - 4t, y = -3 - 5t, z = 8 + 9t OR x = 0 + 4t, y = -3 + 5t, z = 8 - 9t
300
The general form of the equation through the point (0, 3, 5) and perpendicular to the vector <-2, 1, 6>
What is -2x +y +6z -33 = 0?
300
The distance between the planes given by 2x + 4y - 4z = 6 and x + 2y - 2z = 0
What is 1?
300
The angle of intersection between the planes given by 3x + 2y - z - 5 = 0 and 6x + 4y - 2z - 10 = 0
What is 0 degrees?
300
A description of the graph of r(t) = <1 + 2t, -4 + 5t>
What is a line through the point (1, -4) and parallel to the vector <2, 5>?
400
This word ("parallel", "perpendicular", or "intersecting") describes the relationship between the two lines: L1: x = 1 + t, y = 3 - 2t, z = 5 + 9t L2: x = -7 + 2t, y = t, z = 12
What is "perpendicular"?
400
The word ("parallel", "perpendicular", or "neither") which describes the relationship between the planes given by x + 4y + 7z = 3 and 5x - 3y + 2z = 0
What is neither?
400
The distance between the planes given by x + y + z = 1 and x + y + z = -1
What is 2/Sqrt(3)?
400
The coordinates of the intersection of the plane given by 3x + y - z = 0 and the line given parametrically by x = 1 + t, y = t, z = 2t
What is (-1/2, -3/2, -3)?
400
The graph of the equation r(t) = 3costi + 3sintj +tk
What is a helix of radius 3 traveling counter-clockwise?
500
The point of intersection of the lines L1 and L2 given parametrically by: L1: x = -1 + 4t, y = 3 + t, z = 1 L2: x = -13 + 12t, y = 1 + 6t, z = 2 +3t
What is (-17, -1, 1)?
500
The general form of the equation of the plane containing the points (3, 2, 1), (2, 0, 1) and (4, -1, 0).
What is What is 2x - y + z - 9 = 0?
500
The distance between the point (0, 1, -2) and the plane given by 3x + 4y - z - 9 = 0
What is 3/Sqrt(26)?
500
The equation of the plane that makes an angle of 45 degrees with the xz-plane and contains the point (1, 1, 0).
What is y = x OR x - y = 0 OR -x + y = 0
500
The equation of a helix of radius 2 traveling clockwise?
What is r(t) = 2costi - 2sintj + tk?
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