Question

A line passes through the point (2 comma negative 2 comma 10 )​, and is parallel to the vector 9 Bold i plus 7 Bold j plus 10 Bold k. Find the standard parametric equations for the​ line, written using the components of the given vector and the coordinates of the given point.

Answer 1

Title:

The standard parametric equation for the line is $\frac{x - 2}{9} = \frac{y + 2}{7} = \frac{z - 10}{10}$.

Step-by-step explanation:

The standard parametric equation for a line generally represented as $\frac{x - a}{l} = \frac{y - b}{m} = \frac{z - c}{n}$; where (a, b, c) is the point that the line passes through and (l, m, n) is the direction vector of the line.

It is given that the line passes through the point (2, -2, 10).

Hence, here (a, b, c) ≡ (2, -2, 10).

Similarly, the direction vector of the line is given by (l, m, n) ≡ (9, 7, 10).

Putting all the values in the equation of the line, the equation becomes

$\frac{x - 2}{9} = \frac{y + 2}{7} = \frac{z - 10}{10}$.