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Vectors - Coggle Diagram
Vectors
Analysis of vector
Components
Slope
DR
DC
2 vectors
Section formula
vector joining 2 points
Vector along bisector
Intro
Def
Types
Algebra of vectors
Addition
properties
Multiplication by scalar
Product of vectors
2 Vectors
Vector
properties
Applications
Area of parallelogram
a ╳ b where a abd b are sides
(a ╳ b)/2 wher a and b are diagonals
Area of quadrilateral
BD ╳ 1/2 AC where BD and AC are diagonals
Area of traingle
Scalar
properties
geometrical interepetation
projection of a on b
projection of b on a
applications
finding components
along
perpendicular
inding angle between 2 vectors
3 + vecrors
Scalar triple product
Applications
tetrahedron
parallelpiped
properties
reciprocal system of vectors
properties
Vector triple product
Lagrange's identity
Combination of vectors
Linearly independent vectors
Types
A triad of non coplanar vectors
ax + by + cz = 0 for x,y,z = 0
Pair of non collinear vectors
ax + by = 0 for x,y = 0
Def
more than 3 vectors are always linearly independent
Linearly dependent vectors
def
coplanar vectors
If 3 vectors are coplanar then
Theorem 1 : If a and b are non collinear then a vector r coplanar with a and b, the linear combination is xa + yb = r
Theorem 2 : if a, b and c are non coplanar then it can be represented as ax + by + cz =r m