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

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Answer 1 · 2017-12-28T22:56:07

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

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.

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