#### Question

Show that the line through the points (4, 7, 8) (2, 3, 4) is parallel to the line through the points (−1, −2, 1), (1, 2, 5).

#### Solution

Let AB be the line through the points, (4, 7, 8) and (2, 3, 4), and CD be the line through the points, (−1, −2, 1) and (1, 2, 5).

The directions ratios, *a*_{1}, *b*_{1}, *c*_{1}, of AB are (2 − 4), (3 − 7), and (4 − 8) i.e., −2, −4, and −4.

The direction ratios, *a*_{2}, *b*_{2}, *c*_{2}, of CD are (1 − (−1)), (2 − (−2)), and (5 − 1) i.e., 2, 4, and 4.

AB will be parallel to CD, if `a_1/a_2 = b_1/b_2=c_1/c_2`

Thus, AB is parallel to CD.

Is there an error in this question or solution?

Solution Show that the Line Through the Points (4, 7, 8) (2, 3, 4) is Parallel to the Line Through the Points (−1, −2, 1), (1, 2, 5). Concept: Equation of a Line in Space.