Math Problem Statement
Determine whether the lines L _ ( 1 ) and L _ ( 2 ) are parallel, skew, or intersecting. L _ ( 1 ) : ( x
3 ) / ( 1 )
( y
1 ) / (
2 )
( z
1 2 ) / (
3 ) L _ ( 2 ) : ( x
4 ) / ( 1 )
( y + 6 ) / ( 3 )
( z
1 3 ) / (
7 ) parallel skew intersecting If they intersect, find the point of intersection. ( If an answer does not exist, enter DNE. )
( x , y , z )
( , x )
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Parametric Equations
Line Intersections in 3D
Formulas
Parametric form of a line: x = x_0 + t*v_x, y = y_0 + t*v_y, z = z_0 + t*v_z
Checking for intersection: Equate parametric forms of both lines and solve for t
Theorems
Conditions for parallelism: Direction vectors are scalar multiples
Suitable Grade Level
Grades 10-12 (Advanced Geometry/Algebra)
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