MAT1503
ASSIGNMENT 4 2025
DUE: 29 AUGUST 2025 (MEMO)
, ASSIGNMENT 04
Due date: Friday, 29 August 2025
Total Marks: 70
ONLY FOR YEAR MODULE
This assignment covers chapter 2 & 3 of the prescribed book as well as the study
guide, it is based on Study Units 2.1, 2.2, 2.3, 3.1, 3.2 & 3.3 of Chapters 2 & 3 of
HCNote that this assignment will close on 29 August 2025 at 03:00 PM
Question 1
(1.1) Find an equation for the plane that passes through the origin (0, 0, 0) and is parallel to the
plane −x + 3y − 2z = 6.
A plane parallel to −x + 3y − 2z = 6 has the same normal vector (−1, 3, −2).
Through the origin, its equation is:
−x + 3y − 2z = 0.
(1.2) Find the distance between the point (−1, −2, 0) and the plane 3x − y + 4z = −2.
Distance from point P (−1, −2, 0) to plane 3x − y + 4z = −2.
Write the plane as 3x − y + 4z + 2 = 0.
Distance formula:
∣Ax0 + By0 + Cz0 + D∣ ∣3(−1) + (−1)(−2) + 4(0) + 2∣ ∣ − 3 + 2 + 0 + 2∣ 1
d= = = =
A2 + B 2 + C 2 32 + (−1)2 + 42 26 26
1
26
ASSIGNMENT 4 2025
DUE: 29 AUGUST 2025 (MEMO)
, ASSIGNMENT 04
Due date: Friday, 29 August 2025
Total Marks: 70
ONLY FOR YEAR MODULE
This assignment covers chapter 2 & 3 of the prescribed book as well as the study
guide, it is based on Study Units 2.1, 2.2, 2.3, 3.1, 3.2 & 3.3 of Chapters 2 & 3 of
HCNote that this assignment will close on 29 August 2025 at 03:00 PM
Question 1
(1.1) Find an equation for the plane that passes through the origin (0, 0, 0) and is parallel to the
plane −x + 3y − 2z = 6.
A plane parallel to −x + 3y − 2z = 6 has the same normal vector (−1, 3, −2).
Through the origin, its equation is:
−x + 3y − 2z = 0.
(1.2) Find the distance between the point (−1, −2, 0) and the plane 3x − y + 4z = −2.
Distance from point P (−1, −2, 0) to plane 3x − y + 4z = −2.
Write the plane as 3x − y + 4z + 2 = 0.
Distance formula:
∣Ax0 + By0 + Cz0 + D∣ ∣3(−1) + (−1)(−2) + 4(0) + 2∣ ∣ − 3 + 2 + 0 + 2∣ 1
d= = = =
A2 + B 2 + C 2 32 + (−1)2 + 42 26 26
1
26
