Question
Find the equations of the planes that passes through three points:
(1, 1,–1), (6, 4, –5),(–4, –2, 3)
Solution
The equation of line through (1, 1, –1), (6, 4, – 5) is
or
The point (– 4, –2, 3) will lie on this line
if
i.e. if –1 = –1 = –1, which is true
∴ given points (1, 1, –1), (6, 4, – 5), (– 4, – 2, 3) are collinear.
∴ infinite number of planes pass through the given points.
or
The point (– 4, –2, 3) will lie on this line
if
i.e. if –1 = –1 = –1, which is true
∴ given points (1, 1, –1), (6, 4, – 5), (– 4, – 2, 3) are collinear.
∴ infinite number of planes pass through the given points.
