Question

Show that the vectors `4 bb ul a - 8bb ul b` and `-26bb ul a+52bb ul b` are parallel?

Answer 1

`bb ul u` and `bb ul v` are parallel.

Explanation:

Let us assume that the vectors `bb ul u` and `bb ul v` are parallel then there exists `lamda in RR` such that:

`bb ul u = lamda bb ul v`

And using the definitions of `bb ul u` and `bb ul v` we have:

`4 bb ul a - 8bb ul b = lamda(-26bb ul a+52bb ul b)`
`4 bb ul a - 8bb ul b = -26lamdabb ul a+52lamdabb ul b`

Equating coefficients of `bb ul a` and `bb ul b`

`4 \ \ \ = -26 lamda => lamda =- 2/13`
`-8 = 52 lamda \ \ \ \ => lamda = -2/13`

Hence we have found a suitable `lamda = -2/13in RR` such that

`bb ul u = lamda bb ul v`

Hence `bb ul u` and `bb ul v` are parallel.