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# 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⟩

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Parametric equations, polar coordinates, and vector-valued functions asked 2020-12-07
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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