MAT1503
Assignment 4
Due 29 August 2025
, MAT1503 Assignment 04 (Due 29 August 2025)
Total Marks: 70
Chapters: 2 & 3 (Study Units 2.1 to 3.3)
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
To find a plane parallel to another, we use the same normal vector. The normal vector
to the given plane is:
𝑛⃗ = ⟨−1,3,−2⟩
A plane through the origin with this normal vector has the form:
−1(𝑥 − 0) + 3(𝑦 − 0) − 2(𝑧 − 0) = 0 ⇒ −𝑥 + 3𝑦 − 2𝑧 = 0
Answer:
−𝑥 + 3𝑦 − 2𝑧 = 0
1.2
Find the distance between the point (−1, −2,0) and the plane 3𝑥 − 𝑦 + 4𝑧 = −2
The distance from a point (𝑥0 , 𝑦0 , 𝑧0 ) to a plane 𝐴𝑥 + 𝐵𝑦 + 𝐶𝑧 + 𝐷 = 0 is:
|𝐴𝑥0 + 𝐵𝑦0 + 𝐶𝑧0 + 𝐷|
𝑑=
√𝐴2 + 𝐵 2 + 𝐶 2
Rewriting the plane:
3𝑥 − 𝑦 + 4𝑧 + 2 = 0
Plug in values:
Assignment 4
Due 29 August 2025
, MAT1503 Assignment 04 (Due 29 August 2025)
Total Marks: 70
Chapters: 2 & 3 (Study Units 2.1 to 3.3)
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
To find a plane parallel to another, we use the same normal vector. The normal vector
to the given plane is:
𝑛⃗ = ⟨−1,3,−2⟩
A plane through the origin with this normal vector has the form:
−1(𝑥 − 0) + 3(𝑦 − 0) − 2(𝑧 − 0) = 0 ⇒ −𝑥 + 3𝑦 − 2𝑧 = 0
Answer:
−𝑥 + 3𝑦 − 2𝑧 = 0
1.2
Find the distance between the point (−1, −2,0) and the plane 3𝑥 − 𝑦 + 4𝑧 = −2
The distance from a point (𝑥0 , 𝑦0 , 𝑧0 ) to a plane 𝐴𝑥 + 𝐵𝑦 + 𝐶𝑧 + 𝐷 = 0 is:
|𝐴𝑥0 + 𝐵𝑦0 + 𝐶𝑧0 + 𝐷|
𝑑=
√𝐴2 + 𝐵 2 + 𝐶 2
Rewriting the plane:
3𝑥 − 𝑦 + 4𝑧 + 2 = 0
Plug in values:
