Question

prove that necessary and sufficient condition for the vector A,B and C to be co-planer ,if that their scaler tripple vector product A.B×C=0.

Answer 1

a · [b × с] =    1     1     1    =

                         1     3     1  

                         2     2     2  

= 1·2·3 + 1·1·2 + 1·1·2 - 1·2·3 - 1·1·2 - 1·1·2 = 6 + 2 + 2 - 6 - 2 - 2 = 0

Answer: vectors are coplanar as their scalar triple product is zero