+0

# Did I do it correct?

0
228
1
+956

I got :

Sorry if this is a really obvious problem, I'm just insecure with Vectors.

May 3, 2018

#1
+22290
+2

Did I do it correct?

$$\begin{array}{|rcll|} \hline \vec{x} &=& \vec{i} + 2\vec{k} \\ \vec{y} &=& 3\vec{i} + \vec{j} \\ \vec{z} &=& 3\vec{j} + \vec{k} \\\\ && \mathbf{2(\vec{x}-\vec{y})+\vec{z}} \\ &=& 2\left(\vec{i} + 2\vec{k}-(3\vec{i} + \vec{j}) \right)+3\vec{j} + \vec{k} \\ &=& 2\left(\vec{i} + 2\vec{k}-3\vec{i} - \vec{j} \right)+3\vec{j} + \vec{k} \\ &=& 2\left( -2\vec{i} - \vec{j} +2\vec{k} \right)+3\vec{j} + \vec{k} \\ &=& -4\vec{i} - 2\vec{j} +4\vec{k} +3\vec{j} + \vec{k} \\ &\mathbf{=}& \mathbf{-4\vec{i} +\vec{j} + 5\vec{k}} \\ \hline \end{array}$$

May 3, 2018

#1
+22290
+2

Did I do it correct?

$$\begin{array}{|rcll|} \hline \vec{x} &=& \vec{i} + 2\vec{k} \\ \vec{y} &=& 3\vec{i} + \vec{j} \\ \vec{z} &=& 3\vec{j} + \vec{k} \\\\ && \mathbf{2(\vec{x}-\vec{y})+\vec{z}} \\ &=& 2\left(\vec{i} + 2\vec{k}-(3\vec{i} + \vec{j}) \right)+3\vec{j} + \vec{k} \\ &=& 2\left(\vec{i} + 2\vec{k}-3\vec{i} - \vec{j} \right)+3\vec{j} + \vec{k} \\ &=& 2\left( -2\vec{i} - \vec{j} +2\vec{k} \right)+3\vec{j} + \vec{k} \\ &=& -4\vec{i} - 2\vec{j} +4\vec{k} +3\vec{j} + \vec{k} \\ &\mathbf{=}& \mathbf{-4\vec{i} +\vec{j} + 5\vec{k}} \\ \hline \end{array}$$

heureka May 3, 2018