Answer to Question #307578 in Analytic Geometry for Cynthia

Question

Determine if the following lines are parallel, skew or intersecting.

⟨x,y,z⟩=⟨3,2,2⟩+⟨4,5,4⟩t and

⟨x,y,z⟩=⟨5,2,1⟩+⟨ 20,25,20 ⟩t

*If parallel (type the number 1).

*If intersecting (type the number 2).

*If skew (type the number 3).

Blank 1. Calculate the answer by read surrounding text.

Answer 1

⟨x,y,z⟩=⟨3,2,2⟩+⟨4,5,4⟩t

⟨x,y,z⟩=⟨5,2,1⟩+⟨ 20,25,20 ⟩t

Direction cosine of the first line= <4,5,4>

direction cosine of the second line= <20,25,20>

we see that 5V₁=V₂

thus, the lines are parallel.