Cartesian equation of a line

4 The line \(L\) has vector equation $$\mathbf { r } = \left[ \begin{array} { c } 4 \\ - 7 \\ 0 \end{array} \right] + \lambda \left[ \begin{array} { c } - 9 \\ 1 \\ 3 \end{array} \right]$$ Give the equation of \(L\) in Cartesian form.
Tick ( ✓ ) one box.
\(\frac { x + 4 } { - 9 } = \frac { y - 7 } { 1 } = \frac { z } { 3 }\)
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\(\frac { x - 4 } { - 9 } = \frac { y + 7 } { 1 } = \frac { z } { 3 }\)
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-03_108_111_1567_991}
\(\frac { x + 9 } { 4 } = \frac { y - 1 } { - 7 } , z = 3\) □
\(\frac { x - 9 } { 4 } = \frac { y + 1 } { - 7 } , z = 3\) □

11 The line \(l _ { 1 }\) passes through the points \(A ( 6,2,7 )\) and \(B ( 4 , - 3,7 )\) 11

1. Find a Cartesian equation of \(l _ { 1 }\)
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2. The line \(l _ { 2 }\) has vector equation \(\mathbf { r } = \left[ \begin{array} { l } 8 \\ 9 \\ c \end{array} \right] + \mu \left[ \begin{array} { l } 1 \\ 1 \\ 2 \end{array} \right]\) where \(c\) is a constant.
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3. 1. Explain how you know that the lines \(l _ { 1 }\) and \(l _ { 2 }\) are not perpendicular.
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4. (ii) The lines \(l _ { 1 }\) and \(l _ { 2 }\) both lie in the same plane. Find the value of \(c\)