Find the equation to the line which intersects the lines
$x + y + z = 1, 2 x - y - z = 2$
$x + y - z = 3, 2 x + 4 y - z = 4$
and passes through the point $(1, 1, 1)$
The equation is ax + by + cz + d = 0
Find a + b + c - d

Question

Find the equation to the line which intersects the lines

$x + y + z = 1, 2 x - y - z = 2$

$x + y - z = 3, 2 x + 4 y - z = 4$

and passes through the point $(1, 1, 1)$

The equation is ax + by + cz + d = 0

Find a + b + c - d

TestHub · Accepted Answer

The line intersecting the given lines is:

$(x + y + z - 1) + λ (2 x - y - z - 2) = 0 (x - y - z - 3) + μ (2 x + 4 y - z - 4) = 0} \dots\dots\dots (i)$

If it passes through $(1, 1, 1)$ , then we get from (1)

$λ = 1$ and $μ = 4$ .

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub