8.4 Intersections of Lines in Two-Space and Three-Space
Chapter
Chapter 8
Section
8.4
Solutions 19 Videos

Determine the coordinates of the point of interse3ction of the line defined by the parametric equations and the plane defined by the scalar equation.

Q1

Verify that the plane and line are parallel, and then determine if they are distinct or coincident.

\displaystyle \begin{array}{llllllll} &3x + 6y + z -5 = 0 \\ &(x,y, z) = (1, 2, -8) +t(2, -1, -1) \end{array} 

Q2a

Solve each linear system in two-space.

\displaystyle \begin{array}{llllllll} &[x, y] = [-12, -7] + s[8, -5]\\ &[x, y] = [2, -1] + t[3, -2] \end{array} 

Q2c

Verify that the plane and line are parallel, and then determine if they are distinct or coincident.

\displaystyle \begin{array}{llllllll} &x + 2y - 5z + 4 = 0 \\ &(x,y, z) = (10, 3, 4) +t(1, 2, 1) \end{array} 

Q2d

Determine if the plane and line intersect. If so, state the solution.

\displaystyle \begin{array}{llllllll} &3x - y + 4z - 8= 0 &(x,y, z) = (3, 0 , 5) +t(7, -11, -8) \end{array} 

Q3a

Determine if the plane and line intersect. If so, state the solution.

\displaystyle \begin{array}{llllllll} &-2x + 6y + 4z - 4= 0\\ &(x,y, z) = (5, -1, 4) +t(1, -2, 3) \end{array}