Resolution of  Vector

Length of the vector (vl)        
Angle with the component A  along which it shall be resolved (k in degree)        
Find out          
component A length        
component B length ⊥ to A        
Angle the vector makes with component A (ka in degree) : B*sink / (A + B*cosk)        
Angle the vector makes with component B  (kb in degree)        
Vector OA⃗ i + j + k
Vector OB i + j + k
Vector OC i + j + k
Vector AB⃗ i + j + k
Vector BC i + j + k
Vector AC i + j + k
AB x BC i   j   k
BC x AC i   j   k
AB x AC i   j   k
length of AB        
length of BC        
length of AC        
area vector of triangle ABC Δ- (ABxBC +BCxAC +AB*AC) /2; ( AB,BC,AC represent vectors not lengths) i   j   k
Unit Vector ⊥ to the surface of the triangle ABC i   j   k
area  of triangle ABC Δ :        
Find Out        
Determinant (ABC) (a11)   (a12)   (a13)
  (a21)   (a22)   (a23)
  (a31)   (a32)   (a33)
Value of the determinant (ABC)        
length of OA        
length of OB        
length of OC        
Angle between OA & OB (in degree)        
Angle between OA & OC (in degree)        
Angle between OB & OC (in degree)        
Are the vectors co-planar ?        
co-efficient of Vector OB (x)        
co-efficient of Vector OC (y)        
Component of OA along OB (Resolution) i + j + k
Length of OA along OB (AB)        
Component of OA along OC (Resolution) i + j + k
Length of OA   along OC (AC)        
Length of OA        

* If  the 3 vectors are coplanar, then matrix ABC =0 and any vector can be expressed as a linear combination of other 2 vectors

* Any vector can be resolved into 2 components along any other 2 vectors ( not necessarily perpendicular to each other) provided all the 3 vectors are coplanar.