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**Tweety** I really dont understnd this vector problem. please help!

In this question,** i **and **j **are unit vectors in the direction of the positive x- and y-axes respectively.

Given that **a = i – 2j **and **b = –3i + j **find

(a)** λ,** if **a + λb** is parallel to **– i – 3j**

(b) **μ,** if** μa + b **is parallel to **2i + j.**

in the solution bank it shows the answer worked out like this but I just dont get the working.

$\displaystyle xi + yj $ is parallel to $\displaystyle Xi + Yj $ if $\displaystyle \frac{x}{y} = \frac{X}{Y} $

$\displaystyle a + \lambda b = (i - 2j) + \lambda ( -3i + j ) $

$\displaystyle = (1 - 3\lambda)i + ( -2 + \lambda)j $ I dont understand how they got this expression ?