# Intersection of a Line and a Plane in 3.docx - Intersection...

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Intersection of a Line and a Plane in 3-Space Activity 1. a. Line is intersected at the point (3, -7,5) so: Line should not be parallel to the plane (3, -7,5) lies on the plane ( a ^ i + b ^ j + c ^ k ) . ( 2 ^ i + 4 ^ j + 7 ^ k ) 0 2 a + 4 b + 7 c ≠ 0 3 a 7 b 5 c = d Equationof planeis ax + by + cz = 3 a 7 b 5 c withcondition of 2 a 4 b 7 c≠ 0
b. Plane ins not intersected by the line Line is parallel to plane Normal vector of the plane is perpendicular to line vector 2 a + 4 b + 7 c = 0 ax + by + cz = disequationof plane with condition 2 a + 4 b + 7 c = 0 c. Plane that the line lies on Point (1, -3,2) lies on the plane . ( 2 ^ i + 4 ^ j + 7 ^ k ) is perpendicular to normal vector a 3 b + 2 c = d 2 a + 4 b + 7 c = 0 Equationof planeisax + by + cz = a 3 b + 2 cwith condition 2 a + 4 b + 7 c = 0
2. a. Plane intersects x-axis at
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