Revise Vectors unit from G.C.E (A/L) Combined Mathematics.
Suppose is the reference point, and are 2 points.
If divides the line segment in the ratio (both are
positive and ), the division can either be internal or external.
Internally
Externally
Direction Cosines
Suppose . Direction
cosines of are where
are the angles makes with axes.
Unit vector in the direction of
.
Because of this:
Direction Ratio
Ratio of the direction cosines is called as direction ratio.
Cross Product
is the unit normal vector to and . Direction is based on
the right hand rule.
Cross products between , , are circular.
Properties
Scalar Triple Product
iff , , are coplanar. Swapping any 2 vectors will
negate the product.
Vector Triple Product
Resulting vector lies in the plane that contains and