MAT1503 Assignment 04 2025 (Exceptionally Crafted) Due 29 August 2025

MAT1501
Assignment 04
Friday, 29 August 2025

,Student Name: MAT1501 Assignment 04


MAT1501 Assignment 04
Due: Friday, 29 August 2025



Question 1

1.1 Plane through the origin parallel to −x + 3y − 2z = 6

Problem Statement: Find an equation for the plane that passes through the origin
(0, 0, 0) and is parallel to the plane −x + 3y − 2z = 6.

Step 1: Parallel planes share the same normal vector. The given plane has normal


n = (−1, 3, −2).


Step 2: A plane with normal n that passes through the origin has equation


− x + 3y − 2z = 0.


Step 3: This equation satisfies both conditions: same normal (parallel) and passes
through the origin.

Final Answer:
−x + 3y − 2z = 0




Page 1

, Student Name: MAT1501 Assignment 04


1.2 Distance from P = (−1, −2, 0) to 3x − y + 4z = −2

Problem Statement: Find the distance from (−1, −2, 0) to the plane 3x − y + 4z =
−2.

Step 1: Write the plane as Ax + By + Cz + D = 0:


3x − y + 4z + 2 = 0 ⇒ (A, B, C, D) = (3, −1, 4, 2).


Step 2: The distance formula is

|Ax0 + By0 + Cz0 + D|
d= √ .
A2 + B 2 + C 2


Step 3: Substitute (x0 , y0 , z0 ) = (−1, −2, 0):

|3(−1) + (−1)(−2) + 4(0) + 2| | − 3 + 2 + 0 + 2| 1
d= p = √ =√ .
2 2
3 + (−1) + 4 2 9 + 1 + 16 26


Final Answer:
1
d= √
26




Page 2