8.4 Intersections of Lines in Two-Space and Three-Space
Chapter
Chapter 8
Section
8.4
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Lectures 4 Videos
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.

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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}

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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}

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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}

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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}

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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}

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Q3b

Determine the number of solutions for each system without solving.

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Q3c