Question

A plane passes through the points (2, 0, 0), (0, 3, 0) and (0, 0, 4). The equation of the plane is _______________.

Answer 1

Suppose equation of plane is a(x − x₁) + b(y − y₁) + c(z − z₁) = 0
Where plane passes through (x₁, y₁, z₁)
Given plane passes through (2, 0, 0), (0, 3, 0) and (0, 0, 4)
i.e. a(x − 2) + b(y − 0) + c(z − 0) = 0 ...(1)

Since equation (1) passes through (0, 3, 0) and (0, 0, 4)
We get, a(0 − 2) + b(3 − 0) + c(0 − 0) = 0
i.e. −2a + 3b = 0 and a(0 − 2) + b(0 − 0) + c(4 − 0) = 0
i.e. −2a + 4c = 0
i.e. a = 2c and 3b = 2a = 4c
∴ equation of plane is 2c(x − 2) + $\frac{4}{3}$c (y − 0) + c(z − 0) = 0
2(x − 2) + $\frac{4}{3}$y + z = 0
i.e. 2x + $\frac{4}{3}$y + z − 4 × 3 = 0
i.e. 6x + 4y + 3z − 12 = 0 is the equation of the plane