Question

If A vector * B vector = C vector * B vector. Prove that A vector = C vector​

Answer 1

Answer:

I think the proper term is vector a . ( vector b × vector c).

Now vector b × vector c is a new vector whose magnitude is bcsin@ (where @ is the angle between b and c) and this new vector will be perpendicular to both b and c by the definition of cross product of two vectors.

We will call this new vector d. That is , vector b × vector c = vector d.

Now vector a . ( vector b × vector c) = vector a . vector d.

Since vector d is perpendicular to both vector b and vector c , it will be perpendicular to vector a as well becuause all three given vectors are coplanar according to the question.

So vector a . vector d =0

Hence , vector a . ( vector b × vector c) will ALWAYS be 0 no matter what the individual magnitudes are , if ALL three vectors are coplanar.

i hope it helps;)