MAT2615
ASSIGNMENT 1
2025
, QUESTION 1
Solution:
Let ∶ u1 = direction vector of line l1
u2 = direction vector of line l2
∴ u1 = (1,0,1) and u2 = (0,1,1)
The normal vector to the plane, n
⃗ is given by
⃗ = u1 × u2
n
i j k
= |1 0 1|
0 1 1
0 1 1 1 1 0
= i| | − j| |+k| |
1 1 0 1 0 1
= (0 − 1)i − (1 − 0)j + (1 − 0)k
= −i − j + k
= (−1, −1,1)
The equation of a plane is given by
⃗ ∙r=n
n ⃗ ∙ ro
Since l1 is contained in the plane lets choose ro = (1,0,0) then
(−1, −1,1) ∙ (x, y, z) = (−1, −1,1) ∙ (1,0,0)
−x − y + z = −1 + 0 + 0
ASSIGNMENT 1
2025
, QUESTION 1
Solution:
Let ∶ u1 = direction vector of line l1
u2 = direction vector of line l2
∴ u1 = (1,0,1) and u2 = (0,1,1)
The normal vector to the plane, n
⃗ is given by
⃗ = u1 × u2
n
i j k
= |1 0 1|
0 1 1
0 1 1 1 1 0
= i| | − j| |+k| |
1 1 0 1 0 1
= (0 − 1)i − (1 − 0)j + (1 − 0)k
= −i − j + k
= (−1, −1,1)
The equation of a plane is given by
⃗ ∙r=n
n ⃗ ∙ ro
Since l1 is contained in the plane lets choose ro = (1,0,0) then
(−1, −1,1) ∙ (x, y, z) = (−1, −1,1) ∙ (1,0,0)
−x − y + z = −1 + 0 + 0
