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
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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)