Determine whether the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical. r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩

r(t) and s(t) are parallel.

Step-by-step explanation:

Given that :

the  lines represented by the vector equations are:

r(t)=⟨1−t,3+2t,−3t⟩

s(t)=⟨2t,−3−4t,3+6t⟩

The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.

NOTE:

Two lines will be parallel if

here;

Thus;

∴

Hence, we can conclude that r(t) and s(t) are parallel.

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