Vector Questions Flashcards
Area of a triangle
Area = 1/2 |a||b|sin(theta) = 1/2 |a x b|
Area of a rhombus
Area = |a||b| sin(theta) = |a x b|
Volume of a paralellepoid
Rhombus * height = volume, height given from a cos(theta), if b and c are for base, so volume =
|b x c| |a| sin(theta) = a.|b x c|
Distance between point and a line
d = |ro - a| sin(theta) or
d =|v x u|/ |u|, where u is vector and v is vector formed from two points, d is distance.
Points of intersection between lines
Write out each component equation, and then we solve simultaneous equation to give scalars
Intersection between line and plane
We have general equation
Ax +By + Cz = d and line equation, we split line to component, sub in and solve for scalar.
Angle between line and plane
sin(theta) = n.v/|v||n|, where v is the vector for our line and n is the normal from the vector.
Angle between 2 planes
Angle between two normal vectors
Normal vector of a plane
Each coefficient is the component from the = d equation
What are coplanar points?
4 points that all lie on the same plane.
How to show 4 points are coplanar?
Form 3 vectors from the 4 points and show a.(b x c) = 0 where a, b and c is the vector formed from the points
Vector triple
If 3 vectors are on a plane cross product of 2 will be normal, cross product of normal and 3rd vector will be a new vector on the plane
