Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question

Find the line equation(s) of the line(s) through point P (1, 0, 1) that meets
the following line at point(s) at distance 3 from point P0(1, 2, 0).

**Problem #3:** Find the equation(s) of the line(s) passing through the point \( P(1, 0, 1) \) that intersect the given line at a distance of 3 from the point \( P_0(1, 2, 0) \). The line \( L \) is defined by the parametric equation: \[ L: \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} + t \begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix} \] where \( t \) is a parameter. **Explanation of the Parametric Equation:** - The line \( L \) is described in vector form, where: - \(\begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}\) represents a point on the line. - \(\begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}\) is the direction vector of the line. - As \( t \) varies, it generates different points along the line.
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Transcribed Image Text:**Problem #3:** Find the equation(s) of the line(s) passing through the point \( P(1, 0, 1) \) that intersect the given line at a distance of 3 from the point \( P_0(1, 2, 0) \). The line \( L \) is defined by the parametric equation: \[ L: \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} + t \begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix} \] where \( t \) is a parameter. **Explanation of the Parametric Equation:** - The line \( L \) is described in vector form, where: - \(\begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}\) represents a point on the line. - \(\begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}\) is the direction vector of the line. - As \( t \) varies, it generates different points along the line.
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