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Plane through a point
a(x − x₁) + b(y − y₁) + c(z − z₁) = 0
Where: a = Plane through a point, b = b, c = y-intercept, x = x, x₁ = x₁, y = y, y₁ = y₁, z = z, z₁ = z₁
Solved example
Given: b = 7, c = 5, x = 10, x_1 = 4, y = 3, y_1 = 8, z = 6, z_1 = 2
Find: a (Plane through a point)
- Formula: a·(x - x₁) + b·(y - y₁) + c·(z - z₁) = 0
- Rearranged for a: a = (-b·y + b·y₁ - c·z + c·z₁)/(x - x₁)
- Substitute the values: a = (2·5 - 3·7 - 5·6 + 7·8)/(10 - 4)
- Result: a = 2.5
Answer: a = 2.5
Calculator
How to calculate Plane through a point
- Write down the formula: a(x − x₁) + b(y − y₁) + c(z − z₁) = 0.
- Note the known values (b, c, x, x₁, y, y₁, z, z₁).
- Substitute them and simplify to find a.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Plane through a point?
The formula is a(x − x₁) + b(y − y₁) + c(z − z₁) = 0, where a = Plane through a point, b = b, c = y-intercept, x = x, x₁ = x₁, y = y, y₁ = y₁, z = z, z₁ = z₁.
What is Plane through a point when b = 7, c = 5, x = 10, x_1 = 4, y = 3, y_1 = 8, z = 6, z_1 = 2?
a = 2.5. Substitute the values into a(x − x₁) + b(y − y₁) + c(z − z₁) = 0 and simplify.