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.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.