Equations of lines & planes in geometric space Flashcards
1
Q
Give 1 example of a line in 2D vector space.
A
ax + by = 0
2
Q
Give 1 example of a plane in 3D vector space.
A
ax + by + cz = 0
3
Q
How do we know from the equations that we have a vector space?
A
Any combination of two vectors in the space is in the same space.
4
Q
Give 1 example of a line in 2D affine space.
A
ax + by = c
5
Q
Give 1 example of a plane in 3D affine space.
A
ax + by + cz = d
6
Q
Are parallel vectors linearly independent?
A
No.
Therefore their determinant = 0.
7
Q
What can we say about a line that is perpendicular to a plane (edge vectors u and v)?
A
It is parallel to the cross-product of u and v.
