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Quiz 2: Equations of Lines and Planes
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* Indicates required question
Find the general equation of the plane through the points P(1,2,4), Q(1,-1,6) and R(1,4,8)
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1 point
16x-4y = 8
16y = 2
-16x = -16
16x = 16
Given the line x = 0, y = t, z = t and the plane 6x +2y-2z = -3. Find the correct statement.
*
1 point
The line lies on the plane.
The line is perpendicular to the plane and below the plane.
The line is parallel to the plane and below the plane.
The line is perpendicular and above the plane.
The line is parallel to the plane and above the plane.
Find the vector equation of the plane through the origin that is parallel to the plane x = t+p, y = 4+2t-p, z = 4t, where t,p are the parameters.
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1 point
8x+8y-6z = 0
8x+8y+8z = 0
8x-8y+6z =0
8x+8y+6z=0
Given the line x = 0, y = t, z = t and the plane 5x - 3y+3z = 1. Find the correct statement.
*
1 point
The line lies on the plane.
The line is perpendicular to the plane and below the plane.
The line is parallel to the plane and below the plane.
The line is perpendicular and above the plane.
The line is parallel to the plane and above the plane.
Find the general equation of the plane that is parallel to the plane 3x+2y-z = 1 and passes through the point P(1,1,1).
*
1 point
6x+4y+2z = 1
6x+4y-2z = 8
6x+4y-2z = 2
6x+4y-2z = 3
Find the general equation of a plane through the point P(1,1,1) and normal vector n = (3,2,1).
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1 point
3x+2y+z = 1
x+y+z = 6
3x+2y+z = 6
x+y+z = 3
Find a vector equation of the line whose parametric equations are x = 2+4t, y = -1+t, z = t
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1 point
x = (2,-1,0)+(4,1,1)t
x = (2,-1,0)t
x = (4,1,1)+(2,-1,0)t
x = (4,1,1)t
Find a vector equation of the plane with the parametric equation x = 1+2t+p, y = -2-t+5p, z = 4t-p, where t,p are parameters.
1 point
x = (1,-2,0)+(2,-1,4)t+(1,5,-1)p
x = (2,-1,4)t+(1,-2,0)p+(1,5,-1)
x = (1,-2,1)+(2,-1,4)p+(1,5,-1)t
x = (1,5,-1)+(1,-2,4)t+(1,-2,0)p
Clear selection
Determine whether the following two planes are intersecting or not 7x - 2y + 3z = -2 and -3x+y+2z+5 = 0.
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1 point
Yes, the are intersecting.
No, the are parallel.
Yes, the are intersecting. Even more, they are orthogonal.
Which of the following planes, if any, are parallel to the plane x+2y-3z = 2
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1 point
x+2y-3z = 3
1/4x+1/2y-3/4z = 0
x+2y+3z = 2
Find the normal vector of the plane through the points P(1,2,4), Q(1,-1,6) and R(1,4,8)
*
1 point
16
(16,-4,0)
(0,16,0)
(-16,0,0)
(16,0,0)
Given the line x = 0, y = t, z = t and the plane 6x +4y-4z = 0. Find the correct statement.
*
1 point
The line lies on the plane.
The line is perpendicular to the plane and below the plane.
The line is parallel to the plane and below the plane.
The line is perpendicular and above the plane.
The line is parallel to the plane and above the plane.
Find the equation of the line of intersection of the planes 7x - 2y + 3z = -2 and -3x+y+2z+5 = 0.
*
1 point
x = -12-7t, y = -41 - 23t, z = t
x = -7-12t, y = -41-23t, z = -t
x = 12-7t, y = -23-41t, z = t
x = -7-12t, y = -23-41t, z = -t
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