Determine whether the lines L1:x=25+7t, y=17+6t, z=t and L2:x=−12+8ty=−17+8tz=−11+4t intersect, are skew, or are parallel. If they intersect, determine

The lines are skew.

Step-by-step explanation: Two lines can only be parallel OR skew Or intersect each other. To determine that:

1) If the lines are parallel, divide the coefficient that precedes the variable of each equation and compare:

Since they are not equal, L1 and L2 are not parallel.

2) If the lines intersect, when you equal the equations the variable is a valid statement:

25 + 7t = - 12 + 8t (1)

17 + 6t = - 17 + 8t (2)

t = - 11 + 4t (3)

Using (3) to solve the system:

t - 4t = - 11

3t = 11

t =

Substituing t in (1):

25 + 7(11/3) = -12 + 8(11/3)

25 + 77/3 = - 12 + 88/3

Which is not true, so, the lines does NOT intersect.

As they are none of the other options, it can be concluded that the lines L1 and L2 are skew.

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