





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 coplanar ? 





coefficient of Vector OB (x) 





coefficient of Vector OC (y) 





Component of OA along OB (Resolution) 
i 
+ 
j 
+ 
k 
Length of OA along OB (A_{B}) 





Component of OA along OC (Resolution) 
i 
+ 
j 
+ 
k 
Length of OA along OC (A_{C}) 





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. 










