Lines & Planes, Angles & Distance
1. Find a set of (a) parametric equations and (b) symmetric equation of the line through the two points. Find
the point where the line intersects the xy-plane.
(-5, 0,3) , ( 4,-3,2)
2. Find the equation of a plane that contains the line: x = 2-3t, y = 4t, z = -1+ 2t and the point (4, -3, 7).
3. Find the distance between the plane in #2 and the point (-1, 5, -4)
4. Determine if the two planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal,
find the angle of intersection and the parametric equations for the line of intersection.
-3x - 2 y + 2z = 5
x - 3y + 3z = 2
5. Give the equation of the line, in parametric form, that passes through (-3, 1, 11) and is perpendicular to the
x -1 y + 2 z - 2
line
.
=
=
2
3
-2
6. Find the point where the line x = 2-3t, y = -2t, z = 5+3t intersects the plane 2x - y + 4z = 8. Then find the
angle of intersection.
7. Find the distance between the two parallel planes: -3x + 2y -5z = 8 and 6x - 4y +10z = 5
8. Find the equation of the plane that passes through (3, 2, 1), (5, -6, 7) and (4, 1, -7)
9. Find the equation of the plane that passes through the points (-4, 2, 6) and (5, 3, -7) and is perpendicular to
the plane -3x - 2y + 2z = 4 .
10. Given two lines on a plane x = 3+ 2t, y = 4 + t, z = -1+ 2t and
a. Find the point of intersection of the two lines.
b. Give the equation of the plane that contains the two lines.
x -1
z+3
= y-2=
3
3