The adjacent sides of a parallelogram are represented by the vectors vector a = i + j - k and vector b = -2i+ j +2k

Question

The adjacent sides of a parallelogram are represented by the vectors \(\vec a=\hat i+\hat j-\hat k\)  and  \(\vec b=-2\hat i+\hat j+2\hat k.\) Find unit vectors parallel to the diagonals of the parallelogram.

Answer 1

Side BC parallel to

\(\vec{AD}=\vec a, \vec{AB} = \vec b\)

So resultant vector c = b + a

So, vector 

So unit vector along the diagonal of Parallelogram is