# I need help in a simple Vectors question?

## Given that the non-zero vectors a and b are non-parallel and that 3a+t(2a-3b) = a+b+s(a+2b), find the value of t and of s

Mar 19, 2018

$s = \frac{4}{7} , t = - \frac{5}{7}$

#### Explanation:

If $\vec{a} , \vec{b}$ are non parallel then from

$3 \vec{a} + t \left(2 \vec{a} - 3 \vec{b}\right) = \vec{a} + \vec{b} + s \left(\vec{a} + 2 \vec{b}\right)$

we conclude

$\left(2 + 2 t - s\right) \vec{a} - \left(3 t + 1 + 2 s\right) \vec{b} = \vec{0}$

and then

$\left\{\begin{matrix}2 + 2 t - s = 0 \\ 3 t + 1 + 2 s = 0\end{matrix}\right.$

and solving gives

$s = \frac{4}{7} , t = - \frac{5}{7}$