Exercise 1.1.5

Question

Compute $u+v+w$ and $2 u+2 v+w$. How do you know $u, v, w$ lie in a plane? $\begin{array}{l}	ext { These lie in a plane because } \ w=c u+d v . 	ext { Find } c 	ext { and } d\end{array} \quad \boldsymbol{u}=\left[\begin{array}{l}1 \ 2 \ 3\end{array}ight], \quad \boldsymbol{v}=\left[\begin{array}{r}-3 \ 1 \ -2\end{array}ight], \quad \boldsymbol{w}=\left[\begin{array}{r}2 \ -3 \ -1\end{array}ight]$

Prakash Anand · Accepted Answer

$\boldsymbol{u}+\boldsymbol{v}=(-2,3,1)$ and $\boldsymbol{u}+\boldsymbol{v}+\boldsymbol{w}=(0,0,0)$ and $2 \boldsymbol{u}+2 \boldsymbol{v}+\boldsymbol{w}=($ add first answers $)=$ $(-2,3,1)$. The vectors $\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}$ are in the same plane because a combination gives $(0,0,0)$. Stated another way: $\boldsymbol{u}=-\boldsymbol{v}-\boldsymbol{w}$ is in the plane of $\boldsymbol{v}$ and $\boldsymbol{w}$.

Exercise 1.1.5

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Exercise 1.1.5

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