Question

Find the equation of the line through the points (3,4,-7) and (1,-1,6)

• A.
• B.
• C.
• D.

Answer 1

Answer: (B), (D)

The correct options are
B
D

We saw that we can write the equation of a line if we have the direction ratios and a point of the line. We are given two points in the question. Using these two points, we can find the direction ratio of the line joining them.
Direction ratio of the lines segment joining (3,4,-7) and (1,-1,6) = 3-1, 4-(-1), -7-6
= 2, 5, -13
Equation of line passing through (a,b,c) having direction ratios u,v,w is
$\frac{x-a}{u}=\frac{y-b}{v}=\frac{z-c}{w}$
Using the point (3, 4, 7) we get the equation of line as
$\frac{x-3}{2}=\frac{y-4}{5}=\frac{z-(-7)}{-13}$
If we use the point (1,1,-6) instead of (3, 4,-7) we will get the equation as
$\frac{x-1}{2}=\frac{y-(-1)}{5}=\frac{z-6}{-13}$