Calculus & Vectors (MCV4U) · Geometry and Algebra of Vectors

Scalar equation of a plane

Find the value of D in the scalar equation ax + by + cz = D of a plane, given a normal vector or two direction vectors. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MCV4U-GV3.2, MCV4U-GV4.2

Try one

A plane has normal vector n = (4, 3, -6) and passes through the point P = (-5, -3, -4). Find D in the scalar equation 4x + 3y + -6z = D.

Answer: -5

See one solved, step by step

A plane has normal vector n = (4, 3, -6) and passes through the point P = (4, 0, 2). Find D in the scalar equation 4x + 3y + -6z = D.

📘 Worked solution
1D = 4(4) + 3(0) + −6(2)Since P lies on the plane, its coordinates must satisfy the scalar equation.
2= 4Evaluate the arithmetic.

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