MAT1503
Assignment 4
Unique No:
Due 29 August 2025
, MAT1503
ASSIGNMENT 04
Due Date: Friday, 29 August 2025
Question 1
1.1 Equation of a Plane through the Origin Parallel to a Given Plane
The given plane is:
−𝑥 + 3𝑦 − 2𝑧 = 6
For two planes to be parallel, they must share the same normal vector. The normal
vector of the given plane is:
𝐧 = (−1,3, −2)
A plane passing through the origin with the same normal vector will have the equation:
−𝑥 + 3𝑦 − 2𝑧 = 0
Answer:
−𝑥 + 3𝑦 − 2𝑧 = 0
1.2 Distance from a Point to a Plane
Point:
𝑃(−1, −2,0)
Plane:
3𝑥 − 𝑦 + 4𝑧 = −2 ⟹ 3𝑥 − 𝑦 + 4𝑧 + 2 = 0
The formula for the distance from a point (𝑥1 , 𝑦1 , 𝑧1 ) to a plane 𝐴𝑥 + 𝐵𝑦 + 𝐶𝑧 + 𝐷 = 0 is:
Assignment 4
Unique No:
Due 29 August 2025
, MAT1503
ASSIGNMENT 04
Due Date: Friday, 29 August 2025
Question 1
1.1 Equation of a Plane through the Origin Parallel to a Given Plane
The given plane is:
−𝑥 + 3𝑦 − 2𝑧 = 6
For two planes to be parallel, they must share the same normal vector. The normal
vector of the given plane is:
𝐧 = (−1,3, −2)
A plane passing through the origin with the same normal vector will have the equation:
−𝑥 + 3𝑦 − 2𝑧 = 0
Answer:
−𝑥 + 3𝑦 − 2𝑧 = 0
1.2 Distance from a Point to a Plane
Point:
𝑃(−1, −2,0)
Plane:
3𝑥 − 𝑦 + 4𝑧 = −2 ⟹ 3𝑥 − 𝑦 + 4𝑧 + 2 = 0
The formula for the distance from a point (𝑥1 , 𝑦1 , 𝑧1 ) to a plane 𝐴𝑥 + 𝐵𝑦 + 𝐶𝑧 + 𝐷 = 0 is:
