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 ⟩

Answer 1

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,

\vec{r_{0}} = (0, 0, 1), \vec{d} =< 4, 7, 0 >

The vector equation of the line is,

\vec{r} = \vec{r_{0}} + t \vec{d}

\Rightarrow \vec{r} =< 0, 0, 1 > + t < 4, 7, 0 >

=< 0, 0, 1 > + < 4 t, 7 t, 0 >

=< 0 + 4 t, 0 + 7 t, 1 + 0 >

=< 4 t, 7 t, 1 >

\Rightarrow \vec{r} =< 4 t, 7 t, 0 >

The parametric equations of a line are, Result :

x = 4 t, y = 7 t, z = 0

Vector equation of a line is,

\vec{r} =< 4 t, 7 t, 0 >

Parametric equations of a line are,

x = 4 t, y = 7 t, z = 0.

Answer 2

Jeffrey Jordon

Answered 2021-11-08 Author has 2064 answers

Answer is given below (on video)

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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⟩

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