Section 12.2 : Equations of Lines
For problems 1 & 2 give the equation of the line in vector form, parametric form and symmetric form.
- The line through the points \(\left( {2, - 4,1} \right)\) and \(\left( {0,4, - 10} \right)\). Solution
- 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
- 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.
- 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
- 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
- Does the line given by \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) intersect the xy-plane? If so, give the point. Solution
- Does the line given by \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) intersect the xz-plane? If so, give the point. Solution