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5. The parametric equations of a plane ?: ??? x = s + t, y = 1 + t, z = 1 ? s. Find a scalar equation of the plane. a) x ? y + z ? 2 = 0 b) x + y + z = 0 c) x ? y + z = 0 d) x ? y + z + 2 = 0 6. Find the intersection point of the two lines: l1:??? x = 5 ? t, y = 4 ? 2t and l2:??? x = 1 + s, y = ?1 + s a) (5, 4) b) (1, ?1) c) (4, 2) d) (1, 1) 7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2] and [x, y, z] = [?1, 4, ?20] + s [0, ?1, 3]: a) (?1, 0, ?8) b) (2, 0, ?3) c) (?4, ?5, ?8) d) (?4, ?5, 1) 8. In three-space, find the intersection point of the two lines: ??? x = 1 + 2t, y = ?3 + t, z = ?3 & ??? x = 2 + 3s, y = ?1 + 2s, z = s a) (1, ?3, ?3) b) (2, 1, ?3) c) (2, ?1, 0) d) (?7, ?7, ?3) 9. By analyzing the normals, determine if the two planes: ?1: x + 2y + 3z ? 3 = 0 & ?2: 2x ? y + z ? 7 = 0 a) intersect in a line b) are parallel and distinct c) are coincident d) intersect at a point

          5. The parametric equations of a plane ?: ??? x = s + t, y = 1 + t, z = 1 ? s. Find a scalar equation of the plane.
a) x ? y + z ? 2 = 0 b) x + y + z = 0
c) x ? y + z = 0 d) x ? y + z + 2 = 0
6. Find the intersection point of the two lines: l1:??? x = 5 ? t, y = 4 ? 2t and l2:??? x = 1 + s, y = ?1 + s
a) (5, 4) b) (1, ?1)
c) (4, 2) d) (1, 1)
7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2] and [x, y, z] = [?1, 4, ?20] + s [0, ?1, 3]:
a) (?1, 0, ?8) b) (2, 0, ?3)
c) (?4, ?5, ?8) d) (?4, ?5, 1)
8. In three-space, find the intersection point of the two lines: ??? x = 1 + 2t, y = ?3 + t, z = ?3 & ??? x = 2 + 3s, y = ?1 + 2s, z = s
a) (1, ?3, ?3) b) (2, 1, ?3)
c) (2, ?1, 0) d) (?7, ?7, ?3)
9. By analyzing the normals, determine if the two planes: ?1: x + 2y + 3z ? 3 = 0 & ?2: 2x ? y + z ? 7 = 0
a) intersect in a line b) are parallel and distinct
c) are coincident d) intersect at a point

5. The parametric equations of a plane ?: ??? x = s + t, y = 1 + t, z = 1 ? s. Find a scalar equation of the plane.
a) x ? y + z ? 2 = 0 b) x + y + z = 0
c) x ? y + z = 0 d) x ? y + z + 2 = 0
6. Find the intersection point of the two lines: l1:??? x = 5 ? t, y = 4 ? 2t and l2:??? x = 1 + s, y = ?1 + s
a) (5, 4) b) (1, ?1)
c) (4, 2) d) (1, 1)
7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2] and [x, y, z] = [?1, 4, ?20] + s [0, ?1, 3]:
a) (?1, 0, ?8) b) (2, 0, ?3)
c) (?4, ?5, ?8) d) (?4, ?5, 1)
8. In three-space, find the intersection point of the two lines: ??? x = 1 + 2t, y = ?3 + t, z = ?3 ??? x = 2 + 3s, y = ?1 + 2s, z = s
a) (1, ?3, ?3) b) (2, 1, ?3)
c) (2, ?1, 0) d) (?7, ?7, ?3)
9. By analyzing the normals, determine if the two planes: ?1: x + 2y + 3z ? 3 = 0 ?2: 2x ? y + z ? 7 = 0
a) intersect in a line b) are parallel and distinct
c) are coincident d) intersect at a point

Added by Jose Francisco C.

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