Vectors Flashcards
What is the scalar product of two vectors?
What is important about the angle that must be considered in the door scalar method?
Angle of both vectors leaving a point
What is the dot product of 2 vectors that are perpendicular?
What is a position vector?
(Directions how to get onto the line) - vector of a point on a line
denoted as a
What is a direction vector?
(Gradient) how to move up and down a line
denoted as b
What is the vector equation for a line in 3D?
What is the vector CD?
Cā>D = d-c
What is the Cartesian equation of a line general form from the vector equation of a line?
What is the vector equation for a plane?
What is the Cartesian equation of a plane (in 3D) ?
What is the geometric interpretation of d in the Cartesian equation of a plane ?
If a, b ,c are the same then the planes are parallel, d determines the location of the plane. The normal vector (a, b,c) determines the direction
how do you calculate the angle between two lines?
- look at the direction vectors of two lines
- scalar product
how do you calculate the angle between 2 planes?
- look at the normal vector of the two planes
- scalar product
make sure you give acute angle (180 - x) if asked
2 equations one point given
what are the 5 possible ways within which 3 planes can intersect?
- all 3 planes parallel
- 2 planes parallel and one cutting through
(no planes parallel) - all points intersect at 1 point
- sheaf: all 3 planes share a common line
- triangular prisim: 3 pairs of straight lines are all parallel
what does a sheaf look like?
what does a triangular prism look like?
How do you determine which of the 5 possible scenarios of intersections are taking place for the 3 planes?
