The vectors `2 hati + 3 hatj , 5 hati + 6hatj and 8 hatj + lambda hatj ` have their initial points at (1, 1). The value of `lambda` so that the vectors terminate on one straight line, is

Explanation

Since the vectors `2hati+3hatj and 5hati+6hatj` have (1, 1) as the initial point, their terminal points are (3, 4) and (6, 7), respectively. The equation of the line joining these two points is `x-y+1=0`. The terminal point of `8hati+lamdahatj` is `(9, lamda + 1)`. Since the vectors terminate on the same straight line, `(9, lamda+1)` lies on `x-y+1=0`.
Therefore,
`" "9-lamda-1+1=0`
or `" "lamda=9`