Determine whether the lines and L1: (x+1)/(1) = (y-7)/(1) =...

Determine whether the lines and $L_1: \frac{x+1}{1} = \frac{y-7}{1} = \frac{z+1}{1}$ $L_2: \frac{x+8}{2} = \frac{y+2}{3} = \frac{z+12}{4}$ intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty. The lines ? Point of intersection: (, , )

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00:01 In this question, we want to determine whether the lines l1, which is x minus 6 over 1, equals y minus 6 over 2, equals z minus 11 over 3, and line 2, which is x minus 4 over negative 3, equals y minus 2 over negative 6, equals z minus 5 over negative 9, intersect, are skew, or are parallel.

00:23 If they intersect, we're going to determine the point of intersection.

00:26 If not, we're going to leave the remaining answer blanks empty.

00:30 So, what do we do to start? well, typically, what i do is i put these in parametric form.

00:39 So what i do is, since all of these expressions are equal to each other, i'm going to set each of them equal to t.

00:46 So i'm going to say x minus 6 over 1 is equal to t.

00:52 I'm going to say y minus 6 over 2 is equal to t.

00:57 And i'm going to have z minus 11 over 3 is equal to t.

01:04 Since they're all equal to each other, i can set them all equal to t.

01:10 And now, i solve each for x, y, and z.

01:13 So what i'm getting is x equals t plus 6.

01:18 I'm getting y equals 2t plus 6.

01:23 And i'm getting z equals 3t plus 11.

01:27 And now i do the same thing with line 2.

01:32 I'm going to set each of these expressions equal to another parameter, perhaps s.

01:38 So x minus 4 over negative 3 is equal to s.

01:43 Y minus 2 over negative 6 is equal to s...

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