The two adjacent sides OA,OB of parallelogram are 2^i+4^j−5^k and ^i+2^j+3^k. The unit vectors along the diagonals of the parallelogram are given by
Given that,
−−→OA=2^i+4^j−5^k
−−→OB=^i+2^j+3^k
Now, one diagonal of a parallelogram
→P=→A+→B
→P=(2^i+4^j−5^k)+(^i+2^j+3^k)
→P=3^i+6^j−2^k
Now, unit vector along the diagonal
^P=→P|→P|
^P=3^i+6^j−2^k√9+36+4
^P=3^i+6^j−2^k7
Hence, the unit vectors along the diagonals of the parallelogram is 3^i+6^j−2^k7