# Multi-Variable Calculus: Linear Combination of Vectors

 PF Gold P: 636 I would like to check my work with you all. 1. The problem statement, all variables and given/known data Let $\vec{u} = 2\vec{i}+\vec{j}$, $\vec{v} = \vec{i}+\vec{j}$, and $\vec{w} = \vec{i}-\vec{j}$. Find scalars a and b such that $\vec{u} =$ a$\vec{v}+$ b$\vec{w}$. 2. Relevant equations Standard Unit Vectors: $\vec{i} = <1,0>$. $\vec{j} = <0,1>$. 3. The attempt at a solution Compute vectors: $\vec{u} = 2<1,0>+<0,1>=<2,1>$. $\vec{v} = <1,0>+<0,1>=<1,1>$. $\vec{w} = <1,0>-<0,1>=<1,-1>$. Setup Scalars: $<2,1> = a<1,1>+b<1,-1>$. $<2,1> = +$. $<2,1> =$. Find Scalars: $a+b = 2$. $a-b = 1$. Thus, a = 3/2 and b = 1/2. Final answer: $\vec{u} = \frac{3}{2}\vec{v}+\frac{1}{2}\vec{w}$. Note: Sorry my vector arrows aren't lining-up very well.