# Chapter 12: Vectors and the Geometry of Space - Section 12.2 - Vectors - Exercises 12.2 - Page 705: 42

$(-6i-9j)+(7i+7j)$

#### Work Step by Step

Let us consider that $u=u_1+u_2$ and $i-2j=a(2i+3j)+b(i+j)$ ...(1) Equate the terms, we get, $2a+b=1; 3a+b=-2$ Need to solve these two equations, so that $a=-3$ Also, $2a+b=-1$ or, $(2)(-3)+b=1$ Thus, $b=7$ From equation (1), we have $a(2i+3j)+b(i+j)=-3(2i+3j)+7(i+j)=(-6i-9j)+(7i+7j)$

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