Equations of lines Find both the parametric and the vector equations of the following lines. The line through (0, 0, 1) in the direction of the vector v = ⟨4, 7, 0⟩

Equations of lines Find both the parametric and the vector equations of the following lines. The line through (0, 0, 1) in the direction of the vector v = ⟨4, 7, 0⟩

Question
Equations of lines Find both the parametric and the vector equations of the following lines. The line through (0, 0, 1) in the direction of the vector \(v = ⟨4, 7, 0⟩\)

Answers (1)

2020-12-08
Step 1 Given: The line through (0, 0, 1) in the direction of the vector\(v = <4, 7, 0>\). To find: Parametric and vector equations of the given line. Step 2 Let, \(\overrightarrow{r_0} = (0, 0, 1), \overrightarrow{d} = <4, 7, 0>\) The vector equation of the line is, \(\overrightarrow{r} = \overrightarrow{r_0} + t \overrightarrow{d}\)
\(\Rightarrow \overrightarrow{r} = <0, 0, 1> + t <4, 7, 0>\)
\(= <0, 0, 1> + <4t, 7t, 0>\)
\(= <0 + 4t, 0 + 7t, 1 + 0>\)
\(= <4t, 7t, 1>\) \(\Rightarrow \overrightarrow{r} = <4t, 7t, 0>\) The parametric equations of a line are, Result :\(x = 4t, y = 7t, z = 0\) Vector equation of a line is, \(\overrightarrow{r} = <4t, 7t, 0>\) Parametric equations of a line are, \(x = 4t, y = 7t, z = 0.\)
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