Question

8. Determine if the following pairs of lines are parallel and distinct, coincident, perpendicular, or none of these. a. \(\vec{r} = (2, 3) + r(-3, 1)\) and \(\vec{r} = (-1, 4) + t(6, -2)\) b. \(x = 1 + 2r, y = -3 - r\) and \(x = 4, y = \frac{1}{3} + 2t\) c. \(\frac{x - 1}{2} = \frac{y + 4}{1}, z = 1\) and \(x = 4, y = 1 + 2t, z = 6\) d. \((x, y, z) = (1, 7, 2) + t(-1, -1, 1)\) and \((x, y, z) = (-3, 0, 1) + t(2, -2, -2)\)

          8. Determine if the following pairs of lines are parallel and distinct, coincident,
perpendicular, or none of these.
a. \(\vec{r} = (2, 3) + r(-3, 1)\) and \(\vec{r} = (-1, 4) + t(6, -2)\)
b. \(x = 1 + 2r, y = -3 - r\) and \(x = 4, y = \frac{1}{3} + 2t\)
c. \(\frac{x - 1}{2} = \frac{y + 4}{1}, z = 1\) and \(x = 4, y = 1 + 2t, z = 6\)
d. \((x, y, z) = (1, 7, 2) + t(-1, -1, 1)\) and \((x, y, z) = (-3, 0, 1) + t(2, -2, -2)\)

8. Determine if the following pairs of lines are parallel and distinct, coincident,
perpendicular, or none of these.
a. r⃗ = (2, 3) + r(-3, 1) and r⃗ = (-1, 4) + t(6, -2)
b. x = 1 + 2r, y = -3 - r and x = 4, y = (1)/(3) + 2t
c. (x - 1)/(2) = (y + 4)/(1), z = 1 and x = 4, y = 1 + 2t, z = 6
d. (x, y, z) = (1, 7, 2) + t(-1, -1, 1) and (x, y, z) = (-3, 0, 1) + t(2, -2, -2)

Added by Daniel G.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Bradley Duda

Step 1

The slope of Line 1 is 3, and the slope of Line 2 is -1. Since the slopes are not equal, the lines are not parallel. To determine if the lines are distinct, we need to compare their equations. The equations are different, so the lines are distinct. To determine if Show more…

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8. Determine whether the following pairs of lines are parallel, distinct, coincident, or perpendicular: a) Line 1: y = (3x) + K-3, Line 2: y = (-1x) + (6.-2)bK = [48-- ~rand_ = ILy= } +31 c. 5 Xanda =46,}=1+2.256 4 (,070.7.21+K-1.-1. I) and (cX.a =(-10 0)+i