Find the cartesian equation of the line passing through the point $A (2, - 6, 4)$ and parallel to the vector $3 i + 5 j + 7 k$

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Solution

Cartesian equation
$\frac{x - x_{1}}{a_{1}} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
$(x_{1}, y_{1}, z_{1}) = (2, - 6, 4)$
$a = 3; b = 5$ and $c = 7$
$\frac{x - 2}{3} = \frac{y + 6}{5} = \frac{x - 4}{7}$ .

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