If ` vec a= hat i+2 hat j+3 hat k` and `vec b=2 hat i+4 hat j−5 hat k` represent two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram.

Answer

A, B, C

Explanation

Last term in the nth row is
`1+2+3+…+n=1/2n(n+1)(1)`
As terms in the nth row forms an A.P. with common differences 1,so
First term = Last term -(n-1) (1)
`=1/2n(n+1)-n+1`
`=1/2(n^(2)-n+2)` (2)
Sum of terms`=1/2n[1/2(n^(2)-n+2)+1/2(n^(2)+n)]`
`=1/2n(n^(2)+1)`
Now, put n=20 in (1),(2),(3) to get required answers.