Vectors Flashcards
How to calculate the scalar product?
It equals mod a x mod b x cos theta.
What are the properties of the scalar product?
It is commutative so the order in which the multiplication is done does not matter.
When does the scalar product give theta?
This is when the two vectors are directed towards the same point.
When does the scalar product give 180+theta?
When the vectors are directed towards different points.
What characteristics do 2d lines have?
They are either parallel or interesecting.
What characteristics do 3d lines have?
They are either parallel or intersecting or skew.
What are skew lines?
They are 3d lines which are neither parallel or intersecting
How do we know if two lines are parallel?
We can find this out if the direction vectors are multiples of each other.
How to find angle between two lines?
Use the scalar product on their direction vectors.
What is the vector product used for?
It is used to find the normal unit vector to two vectors.
Characteristics of the vector product?
- Anti commutative
- Can be distributed over vector addition
- Scalar multiplication compatible.
How to calc angle between line and plane?
90*-Angle between direction vector and normal because it is angle between line and orthogonal projection on plane.
