What is the real plane R2 composed of?
All ordered pairs of real numbers.
What three properties characterize a geometric vector from A to B?
Magnitude, direction, and orientation from A to B.
What is the zero vector in geometric terms?
It is the vector with magnitude zero representing all such vectors including every vector AA.
What does Chasles' relation state for points A, B, and C?
What defines an orthonormal frame in the plane and space?
Standard vectors are unit length and mutually orthogonal.
What is the formula for the norm of a vector (x,y,z) in R3?
When are two vectors considered collinear?
When one is a real scalar multiple of the other.
What condition defines three points A, B, and C as aligned?
Vectors AB and AC are collinear.
What is the dot product formula for vectors in R2?
It is for u = (a1,a2) and v = (b1,b2).
When are two vectors orthogonal based on their dot product?
They are orthogonal if their dot product is zero.
Answer 10 questions on Vectors, Products, and Subspaces.
1. Which description correctly defines the real plane ?
2. Which three features characterize the geometric vector from point A to point B?
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