Question

Is the line through (−4, −6, 1) and (−2, 0, −3) parallel to the line through (12, 20, 7) and (7, 5, 17)?

Answer 1

yes

Explanation:

A line is a one-dimensional figure having no thickness and extends infinitely in both directions.

Direction ratios of the line joining points
`\left ( x_1,y_1,z_1 \right )\,,\,\left ( x_2,y_2,z_2 \right )` are given by
`\left ( x_2-x_1,y_2-y_1,z_2-z_1 \right )`.

Direction ratio is a number proportional to the direction cosine.

Direction ratios of a line joining points (−4, −6, 1) and (−2, 0, −3):

`\left ( -2+4,0+6,-3-1 \right )=\left ( 2,6,-4 \right )`

Direction ratios of a line joining points (12, 20, 7) and (7, 5, 17):
`\left ( 7-12,5-20,17-7 \right )=\left ( -5,-15,10 \right )`

Ratios of the direction ratios:

`(2)/(-5)=(6)/(-15)=(-4)/(10)=(2)/(5)`

We know that two lines are proportional if their direction ratios are proportional.

So, the given lines are parallel.