Pauls Online Notes
Pauls Online Notes
Home / Calculus II / 3-Dimensional Space / Equations of Lines
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 6-2 : Equations of Lines

For problems 1 & 2 give the equation of the line in vector form, parametric form and symmetric form.

  1. The line through the points \(\left( {2, - 4,1} \right)\) and \(\left( {0,4, - 10} \right)\). Solution
  2. The line through the point \(\left( { - 7,2,4} \right)\) and parallel to the line given by \(x = 5 - 8t\), \(y = 6 + t\), \(z = - 12t\). Solution
  3. Is the line through the points \(\left( {2,0,9} \right)\) and \(\left( { - 4,1, - 5} \right)\) parallel, orthogonal or neither to the line given by \(\vec r\left( t \right) = \left\langle {5,1 - 9t, - 8 - 4t} \right\rangle \)? Solution

For problems 4 & 5 determine the intersection point of the two lines or show that they do not intersect.

  1. The line given by \(x = 8 + t\), \(y = 5 + 6t\), \(z = 4 - 2t\) and the line given by \(\vec r\left( t \right) = \left\langle { - 7 + 12t,3 - t,14 + 8t} \right\rangle \). Solution
  2. The line passing through the points \(\left( {1, - 2,13} \right)\) and \(\left( {2,0, - 5} \right)\) and the line given by \(\vec r\left( t \right) = \left\langle {2 + 4t, - 1 - t,3} \right\rangle \). Solution
  3. Does the line given by \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) intersect the xy-plane? If so, give the point. Solution
  4. Does the line given by \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) intersect the xz-plane? If so, give the point. Solution